More gain would help. I have 200-Ohm mics that give higher output and trigger VOX systems easier, but they sound lousy, and 600-Ohm mics that are excellent in quality, but it is harder to trigger VOX with them, so higher gain would be good. I considered a second stage, but the goal is 'simple as possible'. Adjustable gain is easy enough to get (variable resistor on emitter) but in practice it would be hard to have that and be water resistant too. Besides, I think this is about all you can expect from a single stage. Changing the C-B feedback resistor really doesn't have much effect on gain as far as I can tell. Different transistors (garden variety NPNs) don't seem to make a difference either.
I think higher gain is the definition of 'improve' in this case.
You mentioned noise/wind rejection. How would you achieve that other than mechanical means? I find that filters take out as much voice as wind since they are very similar in frequency when I've done FFT analysis on the separate and combined signals. There are excellent active systems on the market now that I could integrate, but the cost is prohibitive since it requires a processor and power and case, etc.