I'd call the ATF and a lawyer about it. There may be some kind of loophole? With that kind of transfer I think they only charge you the one fee, not one for each can.
If you don't have a trust, now would be a good time to get one and you can let family use them as they please and not be stuck with just one or the other. You'd also only have the one transfer fee. Otherwise if they went to x number of people, you'd need to fill out x number of those forms along with x number of fees, one for each person and his or her allotment of cans.
A good trust or estate attorney familiar with NFA and NFA trusts can square you away with all of this and discuss which method works best for you, and if you get a trust from him, you may be able to get him to handle the other stuff for you too. That's what I'd do in your position.
Check with attorney if this will work first! Another option would be to get a trust now for your dad. He'd have to go sign the documents. You could both be listed as grantors. When he dies, show the attorney the death certificate and he can amend the trust. Note you won't be able to make a purchase without his prints and pictures while he's alive, not with that trust anyway. Same thing with family applies, you can make them beneficiaries, etc., but if they're responsible persons, then they have to do prints and pictures too (unless you temp. revoke them). Check with the attorney first, but if you can set it up where you are the sole grantor and he a trustee, you can remove the trustee and that'd make the cans yours and it'd be even easier. Pretty sure you wouldn't need to bother with a transfer in this case either, but again, check. I'm not an attorney, just sorta familiar with some of these processes, so make sure to talk to one.
Good luck and sorry to hear about your dad. I wish him the best.