A not so minor correction. The heat pumps are not free. The maximum payout is $5000. That has to cover the equipment, installation by a certified professional, and any necessary electrical upgrades. A ballpark estimate for my place comes in at over $6000. If I hold the total cost to $5k, the system will not be fit for purpose under the requirements of the program, making me ineligible for anything.
In addition, your dwelling must be eligible. That sounds easy until you realize that mobile homes must have the axles removed. Hitches, too, but axle removal is the big one. For me, that's another couple of grand to remove skirting, shift blocking, pull the axles out, and replace skirting.
The fact that those axles are useless because of other modifications and additions doesn't change the official designation as a mobile home. I suppose it might be possible to appeal that designation, but I'm not sure that would be less expensive.
For the heat pumps to be truly free, they'd have to nearly double the current subsidy and allow for non-electrical expenses like axle removal.
Your "installer financed" system is sort of like what is available from some solar panel installers. I don't know if it's just a plain lease or rent to own, though.