Our Private Road has six residents and has not had a problem collecting road maintenance fees until recently, when a resident sold to an STR LLC. That entity has delayed paying its road fees. Is the only way to force this LLC to pay it's road maintenance obligations to form an association, in particular, a Statutory Road Association?

The Notice of Claim process that's available to a Statutory Road Association works well if you can wait for payment.  It's worth trying even if you want to be paid right away, because some people will pay when you send them the warning notice letting them know you are about to file the Notice of Claim.  But those who have no intention of paying probably won't do so unless or until they want to either apply for a loan, or sell their property.  If that happens, they will most likely pay because otherwise they won't be able to complete their other transaction.

But you do have another option.  Even if you do not have a Statutory Road Association, you can take them to Small Claims Court, if the amount owed is enough to justify the effort, but is less than $6,000.  You can do that without hiring an attorney.  There's a Guide to Small Claims Cases on the Resources page of the MARA website.