I went to an SBA sponsored match making event which I got to meet the buyer for GSA in my area... She was very nice and encouraging to me, but she claimed she always had to go with the lowest bidder-- which means basically Encap only.-- She did give me some contacts of tenants who sub-rent from the GSA offices and that their hands were tied like hers were.
During this event I learned-- If you want Govt work and or work from big corporations-- Its a plus IF you have a D&B number and Are Not a White Male
We went through something similar here. To get work from provincial government, we had to be iicrc certified, pass a proficiency test, (including a burn test of all fibers you may run across) and then they only accept lowest bid. In the meantime, the janitor is bonnet buffing with Gawd knows what. Waste of time. We have guys charging 6 cents per sqft. Oh, yeah, they want steam cleaning.
If you want GSA work it helps if your a woman, minority, veteran owned business. You wont have to be the cheapest because they will HAVE to throw you a bone now and then, even at a normal "reasonable" price, at least that's how it works on the medical supply side...likely no different on the carpet side. Even then you'll have to build relationships with the decision maker, if they like you, you'll be good to go.