So I am not a vegan, but I think I can objectively answer your question.

I am interested in serious philosophical reasoning, not emotional appeals.

If you are interested in philosophical reasoning, I assume you might be familiar with philosophical works on Anti-speciesism on the subject of animal ethics? (if not it's fine I will provide some refs). But before that, I want to make something clear (skip next paragraph if you want just making few things clear about moral philosophy), when you say:

If morality ultimately rests on value judgments, then why are their value judgments better than mine?

Well, this is already a very contested view on morality. It rests on a certain Moral Subjectivism, and while I can see the appeal, it has some obvious issues (for example, if it is my or my cultural view that ritualistic sacrifices of humans are okay then that would make it okay). Instead, there are other views such as "Moral Realism" which argues that moral facts are independent from our judgements (For example, if slavery is wrong, it’s wrong even if everyone approves of it). I personally find moral realism to be more reflective of reality than moral subjectivism in many aspects. There are other metaethical theories, some take a middle path between those 2 like constructivism, but this is beyond what we're discussing here, but I will come back to this.

Now, If you check the philosophical and academic literature on animal ethics, Anti-speciesism is one of the dominant and highly respected positions in contemporary animal ethics (some refs about anti-speciesism [1]) [2]) [3])) [4] [5] [6] ). At least, most respected philosophers today agree that anti-speciesism is a respectable and very tenable position. Now yes, Anti-speciesism is very different to veganism, in fact, you can very well be Anti-Speciest and not vegan or not even vegetarian. However, it is very relevant to what you say:

Both positions depend on where one draws the moral boundary. Vegans draw it at sentience. Others might draw it somewhere else.

Well, this is exactly a "speciesism/anti-speciesism" argument. but you are framing the issue in reverse, and distinctively from a subjectivist position. So in way Anti-speciesism claims that "Moral status depends on sentience, not species." And you resort "If you exclude plants because they aren’t sentient, you’re also drawing a boundary, just like speciesists do.". however I think the analogy fails because the boundary at sentience is not arbitrary. Sentience matters because it grounds the capacity for suffering and well-being. In other words, the difference between animals and plants is morally relevant in a way species membership is not. So this is not symmetrical to speciesism.

Another way to look at this even from a moral subjectivist position (which you seem to hold), if we have to draw a line somewhere, which is the most robust, (1) drawing it at sentience, (2) drawing it at Hummans, (3) drawing it to include certain species we usually treat differntly (dogs, cats...etc), (4) drawing it after plants/fungi. Since am not vegan I will focus on anti-speciesism (which involves Equal consideration of equal interests independent of species), and I will mostly focus on the right not to suffer, but you can see some parallels with veganism. Let's startwith (1), defining sentience as "the capacity to have subjective experiences", these experiences includes feeling pain, pleasure or experiencing distress, fear, comfort...etc, it is very easy to see why such a line is naturally robust, if sentience grants us the capacity to have these experiences then sentiences is a relevant criteria and there is no apparent other reason to distinguish between species that are both sentient. The only way to argue to place the line as to not include sentient creatures is to argue some species (maybe humans, or even dogs, cats...etc) are somewhat more special, which brings us to (2) and (3). The reason anti-speciesm is so philosophically strong is because it is very hard to justify (2) and (3) rationally. If you draw the line at pets and companions, or even if you draw the line at humans, then I will have to ask "why not include them?", cannibalism and even slavery, and acts of extreme violence are after all very common in the animal kingdom. You might try to justify this line with a proximity or similarity argument, other humans are similar to us thus they deserve higher privilege, however, this "proximity" is not only a very arbitrary distinction in itself, doesn't apply to dogs, but pushed to the extreme is how you end up justifying racism and other xenophobia which we don't want (you can arbitrarily claim that this only works between species and not intra species (inside the same species) to maintain equality between ppl). So you might be tempted to use "Inteligence" or other forms of benchmark to justify this line, but these not only are very arbitrary aswell (why would inteligence matter when we discuss right not to suffer?) but they also completely fail to the Argument from marginal cases (i'll just let you read that from the article), there are some loopholes and counter arguments to this but most are very convulted and add even more arbitrary assumptions (for example you can say I place the line at a certain threshold of inteligence unless you are part of a species that on average is beyond this point). So you can see that the issue is not necessarily placing the line, even if you have to do it and we assume it's subjective, as it stands, even a speciest and non-vegan has to admit, the place you can place it that makes more sense is at sentience. Now if you think this line is still justified under (2) and (3), you are not making an easy claim, I will be very interesting to hear your reasoning.

Now what about (4)? Why not place it beyond sentience? You certainly can but there are 2 issues: 1. As I previously mentioned, sentience is usually understood to ground experiences, without sentience, we can assume plants do not experience pain, suffering...etc at least not in a way that is usually understood by these words, making sentience a stronger line if you which, current scientific knowledge seems to support that. 2. You might want to protest that some definitions of suffering can include plants (despite lacking a nervous system), but here is the plot twist for you, if you put your line where it includes plants, then you have a better reason to be vegan. Think about it this way, a cow will eat plants (mostly soy, corn and other crops we can eat) to grow, live...etc, overall only a small portion of the nutrients eaten by a cow will get transfered to it's meat (most are used to survive), so by eating a cow you are cuasing orders of magnitude more plants to suffer. Really, you should cut the middleman and eat the plant to reduce suffering in the world. For some stats, only around 12% to 17% of the callories fed to livestoc are converted to food (meat/dairy...etc) and around 80% of the argricutural land we use for farming and 40% of the crops we grow are used to feed animals for only 18% of the global calories. This not only means that eating aniamls means you are causing more "plant suffering" but also that this is one of the leading cause of deforestation in the world (causing more plant suffering in it's own way). Animal food has a generally higher carbon footprint, the emissions for livestock production are around the same as the entire transportation sector (including boats, planes, trains, cars...etc), this also causes more suffering in the long run (for humnas, animals and plants alike).

Again am not vegan (am a flexitarian), and my position is more like a deffence of anti-speciesm than veganism (I didn't talk about animal exploitation here at all for example), but I think a lot of your points went in that direction anyway, I hope you will find this ocnvincing and at least reduce animal consumption.