That's a bit odd, after all what would you do if you lived in Nakhon Ratchasima or other Thai towns and cities with long names?
Anyway, as far as I understand it, the post code already tells them that you're in Banglamung:
https://postal-codes.cybo.com/thailand/20150_bang-lamung/
so a postal address like this should work fine:
123/456 Moo 7
Pattaya or Nongprue
20150
where 'Pattaya' or 'Nongprue' is the city, up to you, the postman should know both. I assume that, within the Nongprue tambon, there can only be one 123/456 Moo 7. That ought to be enough for the post office, though definitely not for the delivery people. I have the same problem with a hotel booking website I use, they insist on a city, there are no boxes for tambon and amphur, so I just put Pattaya and it seems to work.