Kathy -
There are many associations that choose to be both non-profit and statutory so as to get the benefits of both. I can't tell you exactly how they do it, but perhaps someone who has done it will jump in on this discussion.
Scott -
Unfortunately, I'm afraid your attorney is mistaken. I am not an attorney, but I'm going to stick my neck out and say so anyway, at the risk of getting chastised by the MARA Board! Section 3121 only kicks in " In the absence of any ... agreement, restriction, covenant, declaration, road association or method elected under section 3101,.." (See section 3121, paragraph 1.) So since you have a road association or agreement already, section 3121 doesn't apply. Here's a link to the statute so you can read it for yourself:
https://legislature.maine.gov/legis/statutes/23/title23sec3121.html
See also paragraph 4 of section 3121, which says that if you already have a road association or agreement, the terms of that road association or agreement control.
Besides, section 3121 requires you to go to court to collect from non-payers, and I believe your existing road association could go to small claims court anyway. Also, section 3121 only allows you to take legal action against a "residential property owner" who does not pay, and it doesn't define what constitutes a residential property. Do undeveloped lots count? The statute doesn't say.