I know money is always an issue but i am a fan of Mitsubishi heating/cooling split units. The idea is a solution of issues like this, its high up, solves minor HVAV small areas that need treated. I am sure for those that ask(without me even looking) relibility should not be a concern being all this really should be considered is a window AC that only switches roles from the condencer to the evap( and visa versa) via coil or some sorta Solid State device. If not for you then somebody else may stumle across this.
I'm a electrician (not that it matters) don't need to get into all the ways you CAN do it, we are about to have a baby so I know what getting the house ready feels like. Obviously heat pumping the the whole house is the way to go. But what you need for now is to just replace it with a base board of the same size. One of the child safe ones that are filled with fluid and protected from little fingers.
Cadets get to hot, regular base boards too. My wife made me yank the baseboards and put in force air with strip heat yikes don't wanna see that bill. Talked her into running the pellet stove one more year and using the forced are fan to circulate. Save up and we will throw in the pump next year. Baby is due in Dec! Our first.