One town, at least, will collect a second mooring fee over and above the NH mooring fee. I'd check, it's a 2nd fee, collected annually.
I see several options. You could have a "tie-off" piling driven to one side of your dock -- probably much less than $500 towards the end of the season. No permit is needed for driving a single piling. There is a electric lift that gets attached to the dock -- $1000, but they appear used for less than half that on
www.nhcraigslist.com. You could use one or two mooring whips -- $125 for one. Or use lag bolts and attach a 2X6 to the dock to use for the bow -- $18. Depending on the cost of the lag bolts.