You can come in close enough to the $100.00 budget to be acceptable and still purchase a great Spray Gun:
A 8.0 neutral Gray Paint mix ($23.00)
Thrifty White Hardboard ($13.00)
"Black Painted" MDF Baseboard Trim ($20.00)
Refine that by wrapping the Trim w/Black Velvet (additional $21.00)
The single most important thing would be to mount the PJ optimally. The 1070 can only be placed at most just over 10.5' away and still maintain an image of 98" diagonal (85" x 48" from the 4' x 8' sheet)
As such, you should not consider mounting it any further back than 10' from the Lens face to the wall.
The 1070 at least has no Image Offset requirements, so by ceiling mounting it with a 12" drop, your 48" tall screen will be placed with the bottom edge at 3' off the ground.
Do you have your Mount selected yet? There are of course several low cost varieties ($40-60.00) that are essentially pretty raw looking collections of Hardware, with limited adjustment potential and no facilitating of Wiring down through the Center.
Then there are choices that cost about 2x the larger amount, but that are rock solid, low profile affairs that allow you to hid the Electrical / Video lines within a 1.5" drop Tube. What with needing at least 12" of drop from the ceiling (...if you do not employ Keystone-ing ...and you don't want to unless absolutely necessary...) and the PJ being situated at least a full 4' out into the room, having a clean, attractive installation will win Brownie Points from the Wife....I assure you.
If you have access above the room via a Attic or Crawl space, I can provided you with simple instructions that will allow you do achieve an almost seamless, smooth transition from out of the Ceiling to PJ, with the Drop Pipe also painted the same color as the Ceiling.
All told, with just a little extra attention to details, and not a very big increase in Budget, you can wind up with an installation that not only looks professionally done, it will still be cost effective. After all, you and others will have to look at the installation when the lights are up, so you really do want it to show off your good judgement and taste.
PS & BTW.....
Unless you can opt to smooth the wall and use it for Screen surface, there are few available options to get you into a larger screen that themselves won't involve spending close to your prescribed budget just tro construct a Frame and purchase the needed substrate. Under 100"? No problems there at all.