Extra powerful boiler short-cycling and overfilling
I have to ask, &quot;who sized the replacement boiler&quot;. An oversized boiler will have numerous operating problems and you are witnessing a few of those problems.
The input of the boiler or as you say &quot;powerful&quot; has little to do with why the boiler water line falls when the boiler fires. The &quot;near boiler piping&quot;, the system piping , the water quality and to a lesser degree the size of the boiler are causing the problems. Was this boiler installed by a licensed boiler installer? Did he flush out the boiler to get rid of the oils and debris that is in the boiler when installed? Is it piped as per the MFG installation booklet? What is the operating pressure on this system? If you have vents on each radiator then you should have a 1 pipe steam system. What controls are installed on the boiler? Has the gas input been set and checked?
Take a few pictures of the boiler and it's piping. Show the size of the piping leaving the boiler and how it is piped. Include pictures of a couple radiators. Oh yes, do not overfill the boiler and I will be interested to see the pictures of the system.
Adding to my answer; if you search for &quot;Arco cast iron radiators (1959)&quot; you should come up with a pamphlet on the size of Arco rads that you can utilize for the heat requirements for your radiators. Even if your rads are not American radiator company rads (arco) you can still utilize this chart since the output will only be a little more or less for another companies rads.
To check the boilers input, it can be done if the boiler will fire long enough to read your gas meter for 1 minute.  With the boiler firing it should use 2.3 cu ft of gas per minute. Your boilers input is 138,000 BTU/hour and natural gas has about 1000 btu/cu ft. So, 1000 btu/cu ft X 2.3 cu ft X 60  minutes  = 138,000 BTU/hour. If the input is too high then you need to get a boiler guy or an HVAC person to adjust the gas input.
Take a picture or 2 of a radiator and post it. Also, the boiler may be oversized but I believe that the boiler needs to be cleaned and skimmed by a professional boiler person. By the way, in what city are you located?