2nd the removable core valves, why would you not use them..
also id say that most non tubeless tyres from maxxis, schwalbe and bonty will work just fine.
there is some logic to your lbs recommending tubeless tyres for this setup because tubeless tyres tend to have a tighter bead fit which is a good thing and can reduce burping, also non tubeless tyres on these rims are often a bit looser unless you use lots of tape or a rim strip.
ztr rims give a tighter fit so non tubless tyres are the preferred option.
its more faff but id try the tape and some non ust tyres and removable core valves before you splash out on ust tyres and rim strips.