Magic Mouse Milk leak stoppers may nurse it through the end of the month, if not the heating season, but it's just a stop-gap to allow contemplation time to get the boiler-swap right.
Taking the opportunity to right-size the new boiler for the actual heat load seems in order. Except for large uninsulated drafty farm houses in the Adirondacks, few houses in NY have true heat loads as high as the 110K+ DOE output of that boiler. Get a room by room heat loss calc done (expect to pay for it, but it's sometimes discounted from the installation price if done by the company that does the swap out.) If that's not possible or likely, the gross sizing can be fairly done using fuel use against degree-day data, using the boiler as the measuring instrument.
If you have a recent gas bill with the exact meter-reading dates on it, it's possible to look up the heating degree days at a nearby weather station during the billing period at degreedays.net. From there you can derive a therms/degree-day number, and convert that to BTUs/degree-day by the boilers nameplate efficiency or AFUE. Dividing that by 24 gives you a BTU/degree-hour factor.
Then, you can look up the
99th percentile outside design temperature for a location near you, and subtract the difference between 65F (the HDD base) and the outside design temp. Then you just multiply the BTU/degree-hour x BTU/degree-hour, and you have a fairly good number to use for a heat load. It's OK to upsize the boiler ~15% from that number if you normally use deep overnight and at-work hour setbacks or only keep the place at 60F, but if the boiler is dripping water on the flame the true efficiency is going to be lower than the boiler's tested ratings (as will the true heat load), so there is already some margin built in.
Don't be shocked if your true heat load come in between 30-60KBTU/hr when measured this way- that would actually be typical of average sized houses with average levels of insulation. Oversizing factors of 2-3x, (even 4-5x) are very common, and end up costing you more up front, and every year thereafter in lower operating efficiency due to unnecessarily large cycling and standby losses. AFUE testing assumes a 1.6x sizing factor, and that's already a HUGE margin above actual conditions. With 1.6x oversizing in a location with a 99% outside temp of 0F would keep up all the way down to -40F, (which is colder than the record lows in those locations.) Even if right-sized only exactly for the 99th percentile heat load you'd still be plenty warm enough, but for the coldest night of the coldest day of the quarter-century it might lose ground, and you may have to suffer through 60-65F indoor temps for a few hours (hours that usually occur while you're asleep in bed), or turn on some electric appliances or a space heater to make up the shortfall.
There's no point to INTENTIONALLY oversizing it, but if one boiler is more than 10% lower in output than your as-used measured number, upsizing it one size within the model line usually isn't an efficiency disaster the way 3-4x oversizing is.
It's a bit unusual for a cast-iron boiler to fail in only 15 years, but not unheard of. If it was run with chronically low return water temperatures creating condensation on the heat exchanger plates it could take an early dive though. If replacing it with cast iron rather than a high efficiency condensing boiler it's worth tweaking the near-boiler plumbing to protect it from low-temp return water. (130F return water would be the absolute min for continuous normal operation for a gas fired cast iron boiler, and many manufacturers won't warranty anything that's been operated continuously under 140F for return water, but most will do just fine forever in the low to mid 130s.)