I don't post much here, but when I see definite safety issues, I get concerns.
Chinboy is on the right track. You have proved that the existing combustion air intake system is inadequate. The use of exhaust fans in the house and the attic ventilation fan definitely make this worse, as would use of fireplace or wood burning stove.
There is a test procedure to determine if existing venting is adequate:
https://www.greenbuildingadvisor.co...fety-and-the-worst-case-depressurization-test
I have worked in the building performance industry, and I have a lot of respect for Martin Holliday and greenbuildingadvisor.com
Found this other quote from Martin: Codes can vary from jurisdiction to jurisdiction, and I am not a code expert on fuel gas codes. That said, here's what I know: "The International Fuel Gas Code requires one of the following options for equipment installed in a mechanical room: either (a) a ceiling duct to provide outside combustion air with a minimum of one square inch of free area for each 4,000 Btu/h input of gas-burning appliances in the room, or (b) a wall duct to provide outside combustion air with a minimum of one square inch of free area for each 2,000 Btu/h input of gas-burning appliances in the room, or (c) a fan that provides 1 cfm of outdoor air for each 2,400 BTU/h of gas-burning appliances in the room."
https://www.greenbuildingadvisor.com/question/water-heater-makeup-combustion-air-source
Info linked above describes the worst case depressurization test, but you MUST find a person certified by BPA and or RESNET to do this. It is very unlikely your HVAC contractor will have this certification.
A quick look suggests the Burnham BS25 boiler is rated at AFUE 85, which has been a code minimum boiler in past years, it would not have any power venting.
As someone implied, I am sure that having 2 gas fired appliances connected to the same vent is not code compliant.
You mentioned replacing your existing water heater with what is known as a "sidearm tank" connected. This will certainly help, and also be more energy efficient as you no longer have 50 gallons of hot water in storage at all times. You can also use a heat pump water heater, which is electric, and efficient, and both NY state and federal tax credits are available for this and other possible remedies for your situation.
https://www.homeefficiencyexperts.c... maximum,including insulation and air sealing
So as I see it you have a sure fix of properly installed sealed combustion appliances for water heater and boiler, or possibly other alternatives. No need to run the depressurization test.
Spend the money and get this fixed, so you can sleep well knowing that both you and your family will wake up in the morning.