If you’re looking for higher lumens in a thrower, I’d say to use the Astrolux FT03 as your starting point of reference. It’s available in the original SST-40, which won’t hit 3000 lumens, but out-throws the newer XHP50.2 version that does hit 3000 lumens. I think there’s also a version of it (FT03S?) that has SBT90.2.
The FT03 is, in my opinion, the next step up from “jacket-pocket” size (though it will surely fit in larger jacket pockets). This is mostly to do with head diameter. It takes a single 26650 or 21700 as you please. The official Astrolux specs are… well, Astrolux specs, so be sure to mentally adjust them down by a factor of something like 25%. Also, if you decide it’s a good form factor, please keep in mind that with A$trolux, you get what you pay for, and read up on the threads devoted to common issues with the light.
Frankly, your price range allows you to get something with better build quality, so I’d recommend the FT03 as a starting point for the research. If you think the head diameter is too large for what you’re interested in, you’ll have to start thinking really hard about the tradeoff between lumen output and throw.