I'm using another mod, Searchlight Assault, which allows turrets to slowly snipe enemies far beyond their normal range when a searchlight spots enemies for them.
I'm not sure if I've ever seen a turret hit when using this sniper-like function, even if I boost default bullet range. The searchlight works on regular turrets, so using dedicated sniper ammo isn't an option for those.

Is there any way Distant Misfires could be altered to play more nicely with Searchlights?

Unfortunately there is no way to alter a projectile's maximum travel distance while the game is running. It's a Factorio API/engine limitation, increasing the bullet range on startup is the only option I'm afraid.

It seemed like there was no distance setting that would allow the projectiles to hit. I don't remember the exact max I tried, but I've never witnessed a hit, although the effect does cause a very slow firing speed. Maybe I'll enable Searchlights again after reaching the sniper ammunition tech. Thank you for your response.

I'm a fan of that mod and I'm aware of potential issues with this combination so I'll definitely look into it as well!

It might have to wait a bit though. I'm trying to catch up on a couple month's worth of patches and mod releases since a medical procedure messed my wrist up.