Here's another recommendation, a new Colt model exclusive to Davidson's Distributor that was released end of last year (link below at Colt's site at bottom of web page) the new Expanse HB series model CE2000HB (black anodized finish).
It have the M4A1 chrome lined medium contour 14.5" mil-spec barrel with long Vortex flash suppressor pinned and welded to meet the 16" civilian law requirement, this model are priced around more or less $661 (in my area of Las Vegas, NV).
There are a few parts that have to be altered or replaced per your specifications, the medium-heavy contour barrel have to be re-profiled to the standard lightweight government contour under the handguards, suggest send it to ADCO for lower cost and faster turn around.
The upper receiver might not have a letter "C" mark, also no T markings on the rail, you could replace it with a real Colt made M4 upper receiver with C marking and T numbers, have ADCO replace it the same time the barrel gets re-profiled.
The hammer, selector, and buffer might have to be replaced, don't really know if these parts are the same with the standard 6920 M4 carbine (these Colt parts are available from Brownells or Specialized Armament Warehouse or other Colt dealers).
Your final cost could be slightly higher than $1K or it might make it if you could get good prices on the replacement Colt parts, either way it would be a great project to get all the features you want.
This new Expanse CE2000HB series are also available in other Cerakote color finishes such as Flat Dark Earth (FDE tan), Tactical Sniper Gray (TSG), Olive Drab Green (ODG), they are $20 more than the black anodized finish.
http://www.colt.com/Catalog/Rifles/Expanse-M4