The other approach is to contact them and agree to pay the corrected amount that you should have paid and ask to have the penalties and interest waived. if you start off agreeing to that then they can collect some money
quickly and move on. If that goes well then add the boat to the mix at that time with the same offer since it could come back again later on.
I had a use tax issue not boat related come up 5 years later once but not in NY. I had moved away from the state 3 years prior. The state had a special division that tracked down use tax collections. Just in case it comes up you need to know moving out of the state won't get you off the hook either if they decide to come after you down the road.
If you take the position that you did pay the use tax and were given every impression that is was fully paid and that this mistake is shared with the DMV for failure to compute the proper tax when you did come forward and agreed to pay it when you did.
You may stand good chance of asking them to accept any difference that you would have paid at the time you paid the DMV had it been disclosed to you what the correct amount was. That amount could include any penalties and interest due up to the time you did pay. This isn't a case where you attempted to dodge the taxes
totally and now got caught.
Tax collectors can waive interest and penalties when the situation shows a case where it is warranted. They don't have the latitude to just forgive the whole tax. Offering to pay the corrected amount is not an unreasonable request. It also would be a good idea to pull together any records that can document the time of the sale
and the exact amount you did pay and when you paid it just in case that becomes an issue. Being prepared before you call them would be advised.