Slightly off-topic, but there are ways to create gmail accounts anonymously. It's a bit harder and well, gmail is owned by Google. But it can be done and then forever accessed through Tor so gmail never has your ip address, except maybe the first time (so the first time, when it is created, you have to do it from some public wifi hotspot or coffee shop or mall.)
You can then use those gmail accounts to maybe sign up for protonmail, maybe? I've only had to make one protonmail account and I don't even use it.
I find it's much easier to hide as a normal looking sheep with the other 1 billion users of gmail.
Crossing international borders is always a risk. I find that the officers don't normally take too much interest in phones or cameras, and sometimes even laptops. As long as you keep all of those devices off and encrypted, they're usually not going to bother. You can also just tape a microsd card to your device without actually inserting it? That way you can "smuggle" up to 1 terabyte of data without anyone knowing.
But, like implied, that might be a hassle for the OP to do.
I wouldn't use anything Google to store anything of value. In this particular case, using gmail throught Tor the way I see it is a recipe for disaster. Google can lock you out at a random time because the IP that you are trying to connect from doesn't match the last device used, which will be the case because Tor always cycles IP's. In fact you can find people with their accounts locked because they tried to log in from an VPN, so I wouldn't even use any proxy to access anything Google, specially if you have an Adsense account. The only way to unlock it would be via doxing yourself (phone) so in this scenario it wouldn't work.
Protonmail is known for handing info when requested, but I guess it's safer when it comes to accessing it thought Tor, even tho I have had Protonmail accounts locked because the IP of the Tor node was tagged by them as "spam", so not even Protonmail is safe from getting locked but at least is less probable than Google. You could also try to get it unlocked via support and pointing to the fact that they even have an onion site so they should support Tor users. No way to do this with Google. I understand the philosophy of hiding between a lot of other users but I don't think Google and Tor get along.
If they decide to ask email or SMS as verification, your only option is either perform the verification or upgrade to paid plan using Bitcoin.
Then I could buy a pre-paid SIM card for a dollar anonymously using cash for the sole purpose of receiving this SMS verification. Or try various disposable email address for verification. Or I could email them and directly request an invite, since the only reason they require verification is to prevent spammers, and it's highly unlikely a spammer is going to email them directly for the purpose of opening a single account. Or I just pay the $5 to open a Plus account for a month, not a big deal.
Although if you are going to encrypt the PSBT before uploading it, you don't even need to use ProtonMail - just host it somewhere you can access via Tor and it won't get deleted. Open a GitHub account and stick it on there. You could probably open a topic on the Archival board here and stick it there. Message it to yourself using an encrypted communication app like Signal. There are multiple possibilities.
Github has banned Tor, or at least the last time I tried you couldn't get past the captcha. Not aware of the Archival method. The main problem would be that you don't control the servers, so even after you delete the file, the file is recoverable. With a strong 128 char random password, it should be safe to say it wouldn't be cracked even if they obtained a physical copy, but you never know.
I was thinking about methods to store a wallet.dat in the cloud too since you can't have the "spawn seed" method like on Electrum, and I just don't feel safe uploading it anywhere even with 128 char sha-512 encryption.
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