I think your better to use at least 2 or 3 projectors.
Anything under 6000 lumen is inexpensive in relation to anything brighter.
You should even be able to find a couple of inexpensive models in the 4000+ lumen range.
This is an inexpensive model i have installed before.
https://www.bhphotovideo.com/c/product/ ... w_aud.html
No one would show up and try to provide audio reinforcement for a stage that size with a pair of home theatre speakers, so why do you think you can try to video map a stage that size and compete with all those stage lights with a 3000 lumen home theatre projector?