Eventually I do want to go back overseas and the timing/circumstances may be as such where I can't be SELRES. Is it possible to do VTU drill at an embassy?
Short answer is "maybe" and you'd be more likely to get "yes" for an answer if you do some of the legwork and make it as easy as possible for your NOSC.
You can reschedule any drill to pretty much anywhere. As for the nuts and bolts of actually doing that, well, since everything went to electronic muster (online) a few years ago, it would be a lot easier if there was a Navy person at the embassy to muster you (the embassy in a lot countries has a mil liaison group with at least one rep from each of the armed services). On paper (in a sense) you'd be reporting for duty to the embassy to do whatever reserve tasks and accomplishments you needed to do. It would probably help to spell everything out in a memorandum of understanding.
Pay close attention to this part:
Even though there is normally no drill pay for VTU drilling, still think of it the same way as paid drills (since there is compensation from retirement points, etc.). The reserves get pretty excited about authorizing and paying drills for unusual circumstances when there is a good opportunity for fraud and too thin a paper trail. Figure out how to mitigate those concerns with procedural controls to reasonably prevent the possibility of fraud. I know that phrase sounds very businessy and managementese, but it would help to look at it from that perspective. The people signing your reserve paycheck like things normal and by-the-book. If you want to drill in a weird place (like an embassy) then you will want to show how your special deal clearly follows the rules. It's been months since I had to GAF about "financial audit readiness," but that's a real thing in reserve personnel management.
The last I heard, NOSC Jax was supposed to have all of the cats and dogs in overseas reserve units (and the NOSC staff is billeted accordingly to handle that). If you asked them about VTU drills at an embassy, I wouldn't be surprised if the first answer you get is "You want do do
what?" but if you've done some homework first then that will help the conversation proceed.
I'm not saying it is definitely possible, but if it could then this is one possible way.