Good question, Ian! You certainly could brown the butter first but as you mention an unknown amount of liquid can evaporate depending on how long it is cooked and even the brand of the butter. For this reason, I generally recommend adding 1-2 teaspoons of water back into the recipe and in the case of cookies, baking one or two at a time to see how much they spread. If not enough spread occurs, then more water is needed. Since you are doing bars, the stakes a bit higher since you can't really bake just one at a time.
 

Still, you could proceed and be very cautious about overbrowning the butter and be sure to use a non-European butter so that the butterfat content is lower and it contains more water. Then, add a tablespoon or so of water into the dough. Because it is baking in a rimmed pan, the spread isn't as much an issue assuming you are able to get it nice and level in the pan prior to baking it. I hope you find this helpful!

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