Figured it out.
Reload time was easy. Just need to change reload_time (and switch_on_delay) in M777_GunsAndAmmo.lua to something reasonable like 180.
The not reloading at all with an unlimited "Fire at Point" task took longer to figure out, but it's because of the multiple launchers (ammo types) defined for the vehicle. That's why the MLRS and M109 didn't have the problem. Seems to be a bug with DCS, reproducible with ED's KS-19. Though I expect no one's come across it because really, who orders AAA to fire at a point on the ground? (EDIT: Correction, the KS-19 *will* reload, it just takes about 20 min, loads all at once, and doesn't appear to reload until its HE rounds are expended. So now I'm not sure if it's just a mod problem or DCS problem, but I've confirmed the fix here works with the latest build)
Quick fix is to comment out (or remove) lines 121-149 in M777LTH_MTVR.lua and lines 90-118 in M777LTH.lua
Longer term fix would be for CH to decide whether to break out the M795 and Excalibur into separate unit definitions as was done for MLRS and HIMARS.