Would that be acceptable, in the sense that it would not break the standard exclusive agreement that I would sign with the exclusive library?
Yes, but the professional thing to do is you should tell the exclusive library that you already sold a few licenses though your own efforts on a “do it yourself/ self publishing” platform. Everyone needs to keep in mind that when you upload, describe, and keyword your own works you are self publishing.
There is nothing wrong with selling and publishing your own works through a 3rd party platform, then removing that same track so you can grant the rights to license that same track to an exclusive publisher.
Also pay attention to words like “your music has never been licensed before” in the new exclusive contract you’d sign. That would make it unacceptable, but I am sure if they really wanted the track and you explained that you already licensed it a few times, that would not be a deal breaker.