If you heat your home with a hydronic system (forced hot water baseboards/radiators/radiant floor) the hands-down best solution for you is an indirect-fired HW tank run as a "priority zone" off the boiler.
Beyond that, a 75gallon tank with a 75KBTU/hr or larger burner would fill the bill, but you may have to crank up the temp a bit, but not much. For more money (but also with a rebate) the high efficiency big-burner 50 gallon Vertex 100 would make it as well.
Tempering valves aren't too expensive, would be a sub-$100 cost adder at the time of installation. IIRC they're now required by code on all HW tank installations in MA- might be in NY too, in which case the point is moot.
A typical 50 gallon tank has about a 35K burner operating at 80% efficiency, delivering ~28KBTU/hr to the water. You're mid-winter incoming water temp is probably ~45F and you're needing to raise it another 65F up to 110F. In the 1/4 hour during the tub fill it's only delivering 7000BTUs to the water, so it's only heating up ~108lbs or ~13 gallons (2 minutes-worth at 5gpm) to 110F, which makes it extremely marginal at best. With a 75KBTU 80% burner behind it you have a tiny bit of margin ,but may have to slow the flow a bit. With a 75gallon tank & 75KBTU/hr 80% burner or the 50gallon Vertex 100 with a 95% efficient burner the margins are much better.