I'm not up on everything by any means...but, if you were to add a chiller and tried to run cold water through your baseboard system, you'd have a real mess on your hands! The condensation would create a huge mess and it wouldn't work very well.
It is possible to run chilled water through a hydro/air heat exchanger, but it needs a fan to move the air into ducts and some means of condensate dispursal/drainage.
There are high velocity, small round duct systems that can be retrofitted, and many choices on minisplit a/c units that may be easier to install in a home that has no existing ductwork.
Basically, you need to move the hot/moist air over a cooler surface, draw some moisture out when it chills the air, then get that air to the room(s) where you need it. Not going to happen with a simple radiator without fan(s). then, you have to deal with the condensate.