Hi op. Don't have POTS but I do have ADHD, so apologies if none of this is useful because I'm not very familiar with POTS.
You might want to have a look at the adhd community on reddit if you haven't already? I did a quick search for the three terms and there was a lot of results.
First comment said Strattera was really bad and made everything much worse.
There seems to be general appreciation for Adderall helping a lot but unfortunately it's not available here unless you have a doc who can prescribe it off label, which will be expensive.
Ritalin seems to get good comments and that is available here.
Vyvanse (Elvanse in UK) is kinda interesting because lots saying it's a lifesaver and no negative effects on POTS. That's what I take myself but my heart rate is definitely up compared to what it is off-meds. No idea how much 'up' is concerning for your condition. I'm assuming that is what the psychiatrist needs cardiologists opinion about?
I checked my fitbit and my average resting hr has gone from 63-65 to 71-73, 78 when I'm not sleeping well (another side effect). Again, no idea if that's helpful or relevant 
It could be that they all work differently for different people - I know that's definitely the case for adhd symptoms and side effects between two people with the same diagnosis. I have a friend happy on Adderall and another one who says it's evil and turned him into a zombie, but copes just fine with Vyvanse.
So I would definitely have a read around with the understanding that it varies so much just for the adhd side of it from person to person.
But it definitely seems like it is working for people so hopefully you can get something to work for you and the UK doctors are willing to try like the US ones. I think it's worth a shot at pursuing?
One more thing I will say is... if you're already struggling with keeping weight on I found medication has made this a daily battle. I have never been a big eater - I used to forget to eat which is probably down to the adhd 😂 - but I was just below the middle of healthy bmi when I went back on medication earlier this year, and now I'm fighting to keep in the green. I have no appetite at all, although I do feel hungry at times... it's a strange feeling. I'm combatting it by having as big a breakfast as possible, and then eating again at 10/11pm at night when I can manage it. But you might find you can tackle it with the little snacks during the day like you've been doing.
Just something to be aware of because I know they monitor this super closely as well as HR and BP in the early days while you go through titration.
Hopefully there was something useful in there and best of luck whatever happens.