Oh this is easy.
Panasonic PT-AR100U 2800 lumen 17' throw = 15 fls with a 1.0 gain screen
The Panny is priced at less than 1/2 your desired budget, making it an ideal choice to upgrade from later without undue remorse.
The best "no upgrade needed" choice? Epson 6010. 2500 lumens 17' - 4" Throw = 26 fls with a 1.0 gain screen
That PJ is borderline a budget-buster, but in all other respects worthy of consideration because of it's terrific Contrast, excellent Lens, both that work to optimize it's lumen output.
BTW, I've used the 6010 on a 185" light Gray screen w/1.3 gain and it never even looked anything less than stupendous.
With the 6010, you can easily remain happy and sated until the 4K machines become reasonably priced.
But....your only dreaming about a Pj suitable for your situation coming with "lens memory". The Panny 7000 is woefully inadequate..................unless you spend mega-bucks on a very large (...and very expensive...) high gain Mfg 2.40:1 screen
That is unless you hunker over to DIY Screens, and I'll show you how to make yourself a 14'er DIY Screen with 1.3 to 1.4 gain. If you do that, you'd wind up with 15 fls
to 16 fls
(...a fl level that is ideal in most peoples' opinions...) w/a 17' Throw. As you already know
Choosing the Panny 7000 , the AR100u, or the 6010 all are made even more desirable if you save outrageously on the humongous screen your aspiring to put up. Your "building" a Theater anyway...why not make a Screen you can be "Suspender poppin' proud" of, eh?