This problem could weaken his heart, so it's not just the tooth and gums that you have to be concerned with.
I can't recommend anything either way except talking to the vet who has been overseeing his heart problem. It sounds like they are doing all the right things to make sure he is safe under anesthesia and they must feel like it is fairly important.
That said, don't hurt yourself financial. Particularly at this age, it's not a great disservice to the pup to leave the tooth in.
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