Sorry for being late to respond...I just bought a house in Colorado!

Saying that the home-buying process is paperwork-heavy when you're self-employed is...an understatement.
Anyway, the honest answer is that I have no idea whether it's possible to take the Pearson Vue version of the GMAT online, and then the Examity version of the GMAT online within fewer than 16 days. However, I do know that the GMAT scheduling system will historically lock you out of whatever's not possible.
In other words, if you can schedule the exam through your MBA.com account, then it's allowed. (Fair warning: this is not necessarily the case for the ETS and the GRE.)
My advice: at this point, why not register for the new Examity version of the GMAT online, starting 4/8/21? The select section order option and instant scoring are well worth the wait, whether or not an ESR option eventually arrives.