Well, you have a driver to sell. I think we can come out on budget. The trick to coming out on budget, is to work with the laws of physics, and not fight them.
I have a design ready to go. I have it in use and I could not be more pleased with it. It is an absolute keeper.
This is the
driver you would need, which takes about half your budget.
It is a transmission line sub, which is very efficient and 100 to 250 watts will power it just fine in a large space.
Here are the pictures.
It was designed as an in wall sub, but does not have to be.
This is the plan. It is 10" deep.
This is the FR.
This is the model.
The unit is powered by a 250 watt amp and it fills a very large space evenly and with ease. TLs have a phenomenally good bass quality.
The boards can be cut at A & K cabinets at Albany MN, where the boards are still in the C & C computer. I'm sure I could find the price and arrange to ship if you don't want to cut the boards yourself.
This is the system it was designed for.