I personally think five stamps on a postcard is abit much, (2nd+2nd+10p+2p+1p) if that’s how you do it.
You can do it with a 1st+50p+10p, save your second class stamps for local mail.
As the US has now moved into World Zone 3 (the most expensive zone), the post office will probably try and discourage you from using the International Economy rate and try an upsell you the £1.70 or even the £3.25 rate!
You are perfect permitted to use the international economy rate, hey mark it with Airmail and see what happens.
Edit: I’ve stopped handing my postcards in over the counter at post offices, I find they take way too much longer, just Bung them in the Post/Pillar Box, they will get there.
A while back I did start to think the postcards I handed over at the counter took much longer and you have confirmed this! I cant see anyone purposefully not sending them with that day’s mail though but I handed one over the counter which is now 26 days to Germany and one I dropped into the post box a week ago has already arrived in Berlin!