If you have something that shows your are here long term, then you can, depending on the branch. Tourist visa and condo lease got me an account at the krungsri branch in the Lotus at On Nut
You’re option is to do the 30 day extension, then either do a border run or a quick 24 trip to another country by air and then do the same process again. 120 days.
Is Bangkok Immigration regularly asking for them? I've been seeing from people that you need it, and some people get extensions in Bangkok without even knowing what that is. Does it kind of just depend on the officer you get or what?