Welcome to the modern age replacing your boiler with modern condensing boilers makes a lot if sense but you will certainly need a very good contractor. A few things first......
The piping design (or lack of) is very critical. Often times the systems are piped with a main supply and return. Each individual radiators will tee off such that the 1st radiator will be the 1st supply and 1st return. The 2nd will be the 2nd supply and 2nd return..... And so forth. The issue is that the 1st radiator can have significantly Less total feet of piping than the last and the flow rates and heating ability of each radiator will be different. This can be changed to a "reverse return" piping arrangement.
Condensing boilers only condense with 'cold' water generally less than 140 degrees. Most systems need to operate at 180 degrees or more and will result in paying a lot of money to get very little efficiency gains...
It sounds like you have a very large home or a very poorly insulated/air sealed home. An absolute must is to have an energy audit done on your home to try and reduce your heat load. Spending thousands in insulation can save you far more money per dollar spent than most any investment you can have. It can also reduce the needed water temperature which will drive up the boiler efficiency. An accurate heat loss in your home is an absolute must!! You at find that by insulating, air sealing, and other improvements will allow you to install 1 boiler and you will have a more comfortable home saving you a fortune.
As for the unit running continuous,,, and modern condensing boiler worth it's weight will fully modulate and run continuous by design. It should run continuously. If you have 2 boilers it will in all likelihood run both boilers simultaneously and modulate with each other. It is not uncommon for your boiler to run 24/7 below say 50 degrees. Since you have zones that may skew the runtime however.