Getting your legal team to send out threatening letters may be manageable, but
the cost of actual pursuit is very high.

filing in a court, at a distance, seeing it through to a judgement, THEN starting to try to
collect... speaking from experience, I can tell you that's a lesson you only need to learn once.

The vast majority of unpaid charges are just written off and not pursued. That is
the case when a business has the resources to bother (but won't because it is rarely
cost effective to do so). When the company is small the likelihood of an ultimately
successful pursuit is near zero.

they may try, and re-try charging the card in the future to capture (more of) the payment,
but you can control this as you already suggested.

this is of course only my opinion. good luck to you.