A full-on replacement of an R22 system is going to require all new refrigierant lines and air handler- it won't be cheap. I might be more financially rational to just recommission it once every 4-5 years by having it thoroughly checked out, including duct leakage, full static pressure tests across the system, refrigerant levels, etc., all the while keeping a "Plan-B" in your back pocket for what the replacement system(s) would be.
IIRC this is a 3-story + basement nearly uninsulated masonry building. It's probably zoned by floor(?), and the sun-drenched upper floor probably has a 1% design load considerably higher than the rest. May houses like this would do pretty well with a mini-split heat pump (ducted or ductless, depending) per floor, each sized for their load. While that would be more expensive than replacing it with another 1-2 stage split system, it's usually cheaper than a fully modulating split system (Carrier Infinity Greenspeed, etc) , and considerably more efficient, more than twice as efficient as your current system, and nearly dead-silent.
At MO type utility rates a standard split system heat pump isn't going to be cheaper than the natural gas boiler for many weeks out of the year, but a modulating mini-split solution can be.
Did you in fact get a full room by room Manual-J heating & cooling load calculation on this place? If not, spending several hundred USD for an engineer or RESNET rater to run aggressive numbers on your place will pay for itself in reduced equipment size immediately, and several times over in the increased efficiency (and comfort) that comes with right-sizing the equipment. You can get a pretty good idea about the whole-house sizing by
data-logging the duty cycle of the 5 ton system on afternoons when temperatures are near the local 1% outside design temperature, but that won't do much for getting the zone-by-zone numbers right.