An exhaust fan would be g'dawful noisy- far noisier than a mini-split with it's blower on "high".
Words like "...only 110-135 CFM ..." are a bit silly without knowing how much you actually need. As with anything, starting with the heat loss calculation of the room you're trying to heat, and which point you could hazard a reasonable guess as to the cfm requirements for moving the heat at some presumed temperature difference.
Assuming there would be at least a 20F difference between the return air and the ceiling air (say 80-85F at the ceiling in the room with the wood stove, 60-65F at the floor of the colder room, every cfm (=60 cubic feet per hour) would deliver (0.18 x 60 x 20= ) 216 BTU/hr. So even a 50cfm whisper-quiet fan could deliver on the order of 11,000BTU/hr into the adjacent room- that's about 1/3 of the heat load of my whole house at 0F outdoor temp, and twice as much as the heat loss of the lossiest room in the house.
Even a 20 cfm fan would probably do fine for a bigger room, a 10 cfm fan for something small. Setting it up with a thermostat at ceiling level to kick it on at say 85F, off at 75F would probably make sense, rather than running it at full power all the time.
But lets' start with the heat loss calculation of the room you're trying to heat- how may square feet of window (and what U-factor or type of window), and how many square feet of exterior wall (and type/R-value), how many square feet of ceiling with nothing but cold attic above (and the R value in the attic)? What's under the floor in that space?
The 99% outside design temp in your area is about +15F, and with the insulated wall/ceiling/floor R-values & surface areas, along with the window area and U-factors we can calculate roughly what it takes to keep it at whatever indoor temp you specify, then either design your ceiling-air loop to meet that using some educated guesses on ceiling & floor temps.
Also, which model Panasonic mini-split? Odds are that even a 3/4 ton mini-split would be able to keep up just fine with the heat load of a room, and probably more cheaply than burning wood in 75% efficiency wood-stove (unless you're managing your own woodlot, and discounting your labor.)