Boat insurance isn't like car insurance. It's not a standard product where everyone's policies are based on the same set of government-issued documents (give or take a few options). Every carrier does something different, and some just won't touch certain markets.
For an older boat, i.e. anything built more than 15 or at most 20 years ago, the only thing to do is keep shopping
around, keep calling independent insurance brokers, until you find one that's willing to deal. Some are willing to insure older boats, but only with a perfectly clean survey
- this is part of why there's a market for shoddy, cursory "insurance surveys" that spit out a valuation and no recommendations. Others will extend liability & comprehensive coverage on-the-hard only until any repairs
stemming from the survey are complete. I'm not sure where the OP is located, but we're happy enough with April Marine
(central Canada) so far for our 45-year-old boat, and Desjardins also made a decent bid with a clever blanket-liability policy that put $1m third-party coverage on the boat itself plus another $1m that would apply to the boat, cars, homeowner's liability, etc. wherever it was needed.
A liability-only policy, for $2m third-party on a $20k boat, would only cost about 1% to 5% more than one which also provides comprehensive coverage of the boat itself on a fair-market-value basis. Hence why almost nobody offers liability-only.
As for taking out a policy for a couple of months and then cancelling, no, they won't let you do that. For policies under about $1k/year in total premiums, there's often (usually?) a 1-year minimum term and the first year's payment is 100% up front.
It's pretty hard to go without it in a developed country. A boat without any insurance stands a good chance of being barred from most marinas
and is frowned upon by bureaucrats, who look at the boat and then look at the potential cost of cleaning
things up if it were to drag anchor
and break up in a seal breeding sanctuary.