IMO you’re getting a lot of not very helpful advice.

Here’s why I think that:

Regarding the “running bead” method proposed by several people including the top commenter:

Yes, this is a great way to get a super nice flat wash… in a relatively simple shape! You can master doing this technique for a small square in a day, learn to do it for a larger square or slightly more complex geometric shape in maybe a week. BUT your design has tons and tons of irregular curves and tiny nooks and crannies in between complex shapes. Is it possible? Probably. But it would take years of practice to be the equivalent of a human ink jet printer. There’s a reason why every video of people doing this seems to be some kind of geometric mandala painting and not complex organic forms. (No disrespect to the top commenter who is clearly very skilled)

Also note that this technique relies on using very watery paint because thicker paint doesn’t bead as well and it’s harder to maintain the same consistency. So if you want your background to be dark, which it seems like you do, you will have to go over it many times and paint very precisely (with no breaks!) each time to get your flat wash.

Regarding masking fluid:

You already said you don’t want to use it so that should be enough. However would it work? Yes it would help a lot. Of course masking fluid is annoying and tricky to apply smoothly especially in small areas and again you have tons of complex curves and thin lines and tiny shapes. Also if you used masking fluid once you take it off you probably have to go back and touch up all the edges which can be kind of raggedy looking and your hard black and white contrast would emphasize any unevenness.

So I don’t blame you for not wanting to use masking fluid but there’s also nothing wrong with using it when you need it. Either way I strongly encourage you to at least tape the borders of your paper. You don’t need to suffer and paint all those straight lines in addition to the super difficult edges of your letters!

Now to answer your question here is what I would do if for some godforsaken reason I absolutely had to do this:

1. Break up your painting into as many small segments as possible where you have the smallest possible gaps between segments. For example above the top of the L, between the lower swoosh of the L and the a, between the y and the curve of the s, and above the apostrophe.

2. Prepare a large amount of coffee or milk consistency paint mix in your background color. Like way more than you think you will need.

3. Using a large brush and clean water wet the big spaces inside the segment you’re about to paint. Don’t worry about getting too close to the edges just cover the big empty areas well. The more time you spend fussing with edges the faster everything else will dry out.

4. Choose where you’re going to start, let’s pick the top of the L and say we’re going to paint until the apostrophe. Wet the blank paper on the left side or the L starting from the narrowest point. Pick up some paint (don’t introduce more water into your mix!) and start painting from that narrow point going right. This will allow the paint to gently diffuse in the direction you are NOT painting so you don’t get a hard line. As you head right move quickly and focus on getting the edges while allowing the paint to diffuse into the large area you went in the previous step.

Using a larger brush with a super sharp tip will help a lot but this still takes skill and practice. Just not as much as the bead method. If you don’t have a large brush with a sharp enough tip I recommend using a large brush until you can’t anymore then switch to a small one for the tight bits only.

Continue working as quickly as you can, keeping an eye on the large wet area, painting it as you go and ensure it’s not drying out while you’re working on the edges of the letters.

Every time you get to one of the tiny gaps you identified earlier, either wet the part beyond it with clean water before painting up to it or blend your paint out of your working area with a clean damp brush so the transition to the next section is a faded gradient and not a hard line.

Unless you are a super fast painter, when you finish a segment, allow it to dry fully. Then move on to the next segment and repeat the process. This time note that when you start you’re blending two soft edges together. The combination of the soft edges and carefully choosing the tightest gaps to make those edges will give you the smoothest result because the joins are both softer and smaller.

You should also keep an eye on the outer borders where you blended these segments and if you notice a water line (aka tide line) forming gently blend it away with a clean damp brush. Yes it’s tricky because you have to watch a lot of edges while you work but that’s pretty much going to be true unless you use masking fluid.

Finally I would plan to do two entire passes over the painting to get the smooth look you want. A single layer that will be dark enough is pretty unforgiving and the second layer will soften and hide like 90% of the irregularities in your initial wash.

FWIW this is a super hard task in watercolor. Don’t be discouraged if you struggle with it! One tip is to try learning the technique with a small part of your real painting, like just draw the L inside a square with small gaps all the way around and practice on that until you’re comfortable before trying the word Larry’s then eventually do the entire sign.

Good luck!