It can be done. It's a lot of trial and error though.

My best results came from the following:

Tape a card down so its borders are covered.
Acetone the crap out of it.
Let dry a bit.
Print a test of the pic.
Cut out pic (leave a little bit of the borders) and tape card in place on the paper (tape goes from the back, though the paper, to the card).
Print with photoshop.

Print settings were as follows:
Max DPI
Least overspray
Mid-low ink
Photoshop manages color
Paper set as HP photo greeting card

It's not perfect, but it came out passable. It almost looks like a real card. You probably couldn't tell the difference with a sleeve. I'll scan the bad jobs and the decent one once they're all dry.

Next, I tried a foil with nearly the same settings. It's a disaster. It's just a mess of runny ink all blurred together. You can only see the vaguest hint of what the card is meant to be. I'm thinking that using less ink and telling it that it's super high glossy paper might work. Dunno. Nice thing about foils is that you can just wipe them and try again

And that's been the project of the day.