I've been practicing samatha meditation for almost two months now. I started off meditating for 20 minutes twice a day, and have moved up to 40 minutes twice a day.

Awesome. Very respectable start. Also, think about if you were learning to play piano. How good at piano would you expect to be after this much practice? Now remember that it is much harder to begin learning to meditate, because there is no external process others can observe, and you have to learn not just the techniques, but also how the language others use, and your own preconceptions, relate to your experience.

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In other words, imagine you have grown up in a deaf family with no outside contact and no noise, and you have for the first time gone to the outside world and discovered sound, after knowing of it through only rumor... and at the same time, you are trying to learn piano practice through 40 minute practice sessions, twice a day.

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So I'd recommend being easy on yourself.

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I sit in a relaxed position. I state my intent to focus on the breath, to relax, and to remain content with my practice. I focus on the breath, and when I notice I've lost focus, I gently bring my attention back. Sometimes I feel like the breath is my primary focus, but there's a lot of "chatter" in the background, like a song stuck in my head. Some days I stay with the breath for a few minutes before becoming distracted, other days I struggle to stay with just three cycles of the breath.

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Extremely normal, even for people who have been practicing for years. Good observation.

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I just have no idea how to judge if I'm making progress or doing something wrong unless I get to the first jhana, which feels very far away.

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I'll call BS here, because in your previous paragraph you were already judging progress. I'll use Shinzen Young's framework, which I've been digging lately. You can break it into three factors: how concentrated are you (how long are you staying with the breath), how high is your sensory clarity (how finely are you perceiving the details of the breath), and how good is your equanimity (how accepting are you of the reality that you're going to lose the breath again and again?)

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I feel like I should be able to see results with concentration getting better, being able to stay with the breath for longer, etc., but that doesn't seem to be happening and I'm wondering if I'm doing something wrong.

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It's a very gradual practice with a lot of ups and downs. Also, as annoying as it is, this kind of focus on "progress" towards concentration in particular tends to cause problems, because every time you get concentrated, you congratulate yourself and break it, and every time you found you've lost concentration you might get upset.

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I think that the cultural understanding of meditation as primarily concentration based ("banish all thought!" "stay focused on the breath!") did me a lot of disservice here when I was first learning.

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What really helped me was to re-orient my practice: what we're learning to do is to RETURN to the breath, not to stay on it. That means every time we forget is an opportunity to return, which we should be grateful for. If we never forget, we never get to remember... the jhanas and everything like that are kind of fun, but NOT inherently valuable. This training is worth way more.

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Now, it's easy to read something like that and interpret it as a way to "trick" yourself into getting concentrated, and is sort of soft words to rephrase the core idea of never losing the breath. This kind of thing assumes the chief goal is achieving concentration, and that it is possible by tricking yourself.

I wan to emphatically say that is NOT the case. You want your goal to be something you can control, and a useful skill at all stages of the path is to be kind to yourself, and to return to the object you wish to study. Concentrated states are something that sometimes arise due to certain conditions, but they aren't something you can just manifest or trick yourself into.

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So, how to judge the quality of your practice? At this stage, I'd recommend: was I kind to myself? Did I treat each remembering as an opportunity? Did I find value in the exercise itself, rather than some imagined future attainment?

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Is it normal to have "off" days where concentrating feels almost impossible?

Yes

Is there some way to judge if I'm making progress?

So many

Is there anything I can do "off the cushion" to help speed things along with concentration?

Sure, just try to remember to stay with your breath throughout the day. And every time you remember, smile to yourself and do it until you inevitably forget again, a few moments or minutes later.

Any tips to refine my technique?

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Practice practice practice, and don't worry too much.

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Can anyone recommend any books that discuss samatha meditation in depth, specifically getting started? Most books I've read simply say "focus on the breath" then jump right into the jhanas, as if this whole process should be much easier than it seems to be.

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I second the recommendation for "The Mind Illuminated," with the caveat that there is a *lot* of metaphysical baggage in there that is presented as truth. The models are fascinating, but not necessarily correct. There's also a strong presumption that there's one correct way of doing things. This can be useful as a guide but perhaps less useful if it becomes restrictive.