Well, here in your second post you’ve answered your own question.
If she has a clearly stated preference of wanting cash then you do that. Or whatever her preference is. Why over complicate matters? If she said she wants cash then you pay with cash and nobody here understands your question.
There are gift cards that will let you put 2k on them. Many many gift cards go up to 500 bucks. How’s that a lot of gift cards?
2k is only a four inch stack if you’re a stripper.
Why are you nervous about carrying it through the airport? If you’re worried about the authorities, everything I’ve read along with my own experience indicates that under 10k nobody cares. If you think you’re going to get mugged or something then calm down and man up. If you really are playing in the $2k+ per session end of the pool, then you probably walk around every day with stuff on you that’s worth more. The other stuff in your wallet, jewelry, watch, car, we all seem to forget about the thousand dollar mini computers in our pockets.
If she’s flying to you why are you carrying it through the airport anyway?
If you’re that scared about it go to the bank when you land.
If you’re so confident that you’re not worried about the electronic paper trail then why ask?
Oh yeah, you asked because you know they want cash but you’re “not comfortable” with that. So your real question seems to be about how to get around provider’s stated policies. Is that about the gist of it all? Well, that’s a dangerous game. Just don’t. Move on and find a provider that accepts zelle or venmo or cashapp. There are plenty of them out there.