So my options now are to install a ductless minisplit system for the downstairs, get the trusses re-engineered to make a bigger opening, or install exposed ductwork. 

If you have exposed duct work, make sure the joints fit together tight and your not losing heat/air into a basement.

Do you remove the radiators and install forced air heat and incur all of the costs of adding duct work?

Here's a list of what got done this week: A/C duct work complete.

The list of things completed $350 - Dumpster rental$0 - did myself laber tore out old kitchen and put in New kitchen$3200 - Replaced all kitchen cabinets (find a contractor friend that can get you cabinets at cost.. saves approx 50%)$1200 - replaced Refridgerator, stove, microwave, added dishwasher, washing machine, (Nicks Used appliances came with 90 day warranty)$3500 - added central Air and had some duct work done. $250 - Paint entire inside of house. $1200 - new carpet in 4 rooms$150 - Updated Kitchen and bathroom lights. $350 - Vinal plank flooring in Kitichen ($0 in Labor did myself) Other Misc stuff including replaced all outlets and covers, closet door replacements and ??

Since there’s no A/C in that property, I’m trying to decide between installing a brand new HVAC system/ductwork for $8,500 or replacing the boiler for $5,500.

Well obviously you can drill holes for the wires, but I would be nervous to drill such a big hole for the ductwork.

Some duct work appears to be wrapped with asbestos.

generally on hvac issues in a small older home i see prices from 4k to 5k for an entire system if ductwork is present. 

I would really see if its just in the duct work or carpets etc and getting blowing around if so just get the duct work cleaned and new air filter provided you have them.