If you're planning on breaking out of a certain contract-type or the other will be even more ridiculous, then consider putting out a separate RFP or having some special setup that allows you to just bypass or do the RFP at a higher rate. I'd recommend putting out an RFP for every project that needs it, even though it's a small number of the projects you're doing, and use that for the next project so the future RFPs won't get wasted. Otherwise you'll always run into these problems of a small number of big companies needing to get approvals because they're the one entity.
It gets complicated but there are some simple rules to follow. If you are running a non-competitive RFP then that might be okay because you are running a competitive RFP and so you get these opportunities to leverage your competitors, use one of the other competitive RFP rules for other projects, to use your competitor's RFP, etc. but you need to make sure the RFP you are running only does what the competition isn't allowed to do.
Having worked with a lot of contracted firms that do custom software development and platform customization, let’s not put them too high on a pedestal. What money you save on FTE programmers needs to be funneled right back into management talent to make sure they deliver a quality product (high utility, supportable by next contractor, quality docs, etc). Good management talent is hard to find and not something any government is known for. Consequently, next contractor probably has mondo ramp-up time deciphering what hacked pos the last guys put in with their c-team developers (cuz margins).
It gets complicated but there are some simple rules to follow. If you are running a non-competitive RFP then that might be okay because you are running a competitive RFP and so you get these opportunities to leverage your competitors, use one of the other competitive RFP rules for other projects, to use your competitor's RFP, etc. but you need to make sure the RFP you are running only does what the competition isn't allowed to do.