All correct GI's for less than $2K...maybe somewhere, but not around here
20 plus years ago I was heavy into milsurps, and 1911's were the cream for me. Then I stumbled into "collecting" (more like accumulating) finer S&W revolvers, starting with a Model 29-2 in 1986.
Anyway....those S&W's were pretty pricey for top drawer specimens (funny........still are)

so some 1911's (all correct, no arsenal rebuilds) had to go:
Colt 1911A1; sold for $2600 Jan 2015
Remington Rand; sold for $2000 December 2013
Argentine Army (built on Colt machinery/Colt supervision) wrong grips, all else correct) sold for $675 December 2017
Ithaca 1943: still here, last one I have: offered $2600 August 2020, offered $2800 last month (same guy)..still here.
I honestly don't think you can beat CMP...yes they are mixmasters, but stupidly scare to find one that isn't these days, and those that do have them know what they've got (and what they paid for it vs what they are worth now).
Added bene of CMP.........those guns have been there and done that so you are still buying history that most probably did see troop unit duty...instead of pristine examples that may have sat in a paymasters drawer.
So yea.....if you really can't wait...just look on the big auction site...seems to me that there are several people that bought from CMP just to markup and make a buck. I personally don't like that practice, but there are a bunch out there in the $1500, $1600 (and up).
I just don't think you will find a "real" GI 1911A1 for less than $2k at least not around here from private sellers.