Your issue with the boiler is one of putting out too MUCH heat, and short-cycling on baseboard heaters more than having too little. If the fuel is propane or oil you'll be better off heating/cooling the room with a mini-split heat pump, but if on natural gas there are water-heater solutions to think about.
I'm seriously doubting the 3500 BTU/hr number unless you're in an unusually warm spot in SW OH, but it's under 10K for sure. Just your windows and door lossed add up to more than 3500 BTU/hr!
The quick & dirty heat load calc runs something like this:
Figuring a 99% outside design temp of +10F, and an indoor temp of +70F that's a 60F delta-T.
Without looking it up, assume the windows have U-factor of about 0.35 BTU/degree-foot-hour, or 60F x 0.35= 21 BTU/hr per square foot. (Unless they're something special and expensive, that'll be close enough.) Each window is 13 square feet, so with 7 windows your window losses are 7 x 13' x 21 BTU/hr= 1911 BTU/hr.
If they're clear-glass (no low-E, no argon fill) the sliders and doors have a U-factor of about 0.5, and a heat loss of 60F x 0.5= 30BTU/hr per square foot. Combined you have 60 square feet of door, for a heat loss of 60' x 30 BTU/ft-hr= 1800 BTU/hr
Assuming you have at least R19 in the ceiling the ceiling U-factor will be less than 0.06 BTU/degree-hour-ft, and with 22x16 = 352 square feet of ceiling that's an upper-bound loss of 0.06 x 60F x 352= 1267 BTU/hr.
With 2x4/R13 construction the U-factor of the walls is about 0.1 BTU per hour per degree-F per square foot. So at a 60F delta that's about 0.1 x 60F= 6 BTU per square foot of exterior wall area. (Make up a spreadsheet, and do the measuring.) If the common-wall to the rest of the house 16' long and you have 9' ceilings, the exterior walls are about 9' x (22' +22+ 16')= 540' of gross wall area, less 91' of window and 60' of door for about 390' of wall area. At 6 BTU/ft- hr that's 2340 BTU/ft-hr
Add it all up and you're at about 3.7K for windows and doors, 3.6K for walls and ceiling for 7.3 KBTU/hr heat load at +10F outdoor temps. With a GENEROUS 30% margin for air leakage and thermal bridging through the slab make that 1.3 x 7.3K= 9.5KBTU/hr max. And there's no way it'll be under 6 KBTU/hr, even with a super-insulated ceiling plus slab-edge insulation.
A pretty-good 3/4 ton mini-split like the Fujitsu AOU-9RLS2 or Mitsubishi MSZ-FE09NA could more than cover that load, and even the smallest boilers would be 5x oversized for that load, and that's probably the best solution here, since you'd also get high-efficiency air conditioning out of the deal. The hardware itself isn't all that expensive, about $1500 at internet pricing. Add another fifty or hundred for bracket mounting or a pouring a concrete pad. As a mostly-DIY maybe $150-200 in reefer-tech time to do the refrigerant charge and initial testing (with all the right tools that you don't want to own, and the experience you probably don't have), you're talking 2 grand. A complete turnkey all-pro installation might run between $2.5-3K. Operating costs will be comparable to heating with an 80% natural gas boiler, maybe a bit less, depending on what your actual gas/electricity rates are.