Im rank 343, trying to find larvae/Caelon and 26 rounds done the 1st mission of the lazuli chain. If I get the 2 tevrazon tracers, I'll be >350 and the dreaded flamehawks will begin to appear. Will their existence reduce my chances of getting good NPCs, such as the above 2 and troop carriers?

No, because they take the place of whatever crimson hawk you see now.

Apparently crimson hawks still last past 350, but presumably only up to 399. I don't want to rank up that much though.

Anyone have some more advice?

Every new npc you can see reduces your chance of seeing the others. If every marble is red, you have 100% chance. Add in 2% blue and now you no longer have 100% on red.

You can reduce your scan, remove mission npcs by completing missions, and out-rank npcs, but that's about it. Just make sure you have the right amount for what you're looking for and pew, pew, pew.

You have to bite the bullet eventually.
NPC away but don't stress when Caelon or the hybrid take a hundred ranks to find.