This one's probably the best for you, since you still have gift slots:
Assuming you have puppets, junk EVERY single non-legendary card (unless it's a highly-profitable card like
Farrakhan; if you pull something valuable, gift to your main and sell it like a normal person would) that each puppet has to make a sizeable number of bank.
After that, you must transfer it by having your main account obtain a stupidly high number of copies of the same card and have said account sell them all to the puppets that have the bank gathered (from junking its cards):
Here's an example:
https://i.ibb.co/FqfkQs6/Fire-Shot-Capt ... es-net.pngI'd advise to only bid 1-2 bank per puppet, since if someone pulls and underasks then you'd only lose that much (plus it allows you to buy an extra copy to use in subsequent transfers for relatively cheap).
Once your puppets buy all your copies of that card, you can then just gift them back to your main and repeat the process.
I've used this strategy for a bit, and it's successfully gotten me around 50-bank transfers (at a time) in broad daylight