Why do you think that it would work? What you share with us is clear:
Why would you think they block MongoDB port and not other DB provider?
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I understand that some of their servers are not blocked and will let you connect. May be you can try that before changing VPN or DB.
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I understand that rather than trying to take care of the abusers, they prefer to block all legitimate users. The sad part is that they do not seem to be inclined to help you.
But networking wise, can’t you simply create a different IP route that bypass your VPN for what ever IP network your cluster is using?