Here's what I used for sound last summer.
It won't necessarily fall in your budget...it will depend in part on some luck and putting other parts together.
I bought the two bass bins for $200 total. My real expense is in the top horn (about $1,000) however, 2 weekends ago, I pulled all this outside and tried it as a 2-way with the large horn playing with the bottom horns and two versions of a 3-way.
First 3-way version was with the LaScala sitting on top and the second 3-way setup was with the LaScala rewired, bypassing the mid/high horns and using ONLY the woofer more as a mid-bass unit before handing off to the large horn on top.
With an active crossover, I was able to have all wired up and with some presaved programs, change between the two or three way setups.
Just showing this to throw some different thoughts.
At 52' I was hitting 114db peaks on my 100% perfectly accurate RS SPL meter
You could build or watchout for some bass bins like this and buy some beater LaScalas and have a killer outdoor system.
Have a lot of friends though because it's a back-killer to move