To get the COP you are looking for, you need to keep the air circulating through the heat pump constantly at that level. If you try to capture all the heat out of it, your COP is going to fall to what the temp leaving the unit is at or close to it. Your either not going to heat your infloor well or your going to dump a lot of heat into your basement. You don't need to waste a bunch of money to find this out.
Get a heat load calc on your house
See if your heat pump can even produce that much heat, at a reasonable COP, off the COP vs temp chart, note the temp needed.
At that temp, calc the cfm needed to move the heat down there, less a heat exchange efficiency.
Check to see if your insert is even close to able to produce that amount of heat, remembering you can't capture anywhere close to 100% with a duct/fan setup.
I'm a real negative sort on this it sounds like but I'd rather see you put money and time into something more workable.
Get a heat load calc on your house
See if your heat pump can even produce that much heat, at a reasonable COP, off the COP vs temp chart, note the temp needed.
At that temp, calc the cfm needed to move the heat down there, less a heat exchange efficiency.
Check to see if your insert is even close to able to produce that amount of heat, remembering you can't capture anywhere close to 100% with a duct/fan setup.
I'm a real negative sort on this it sounds like but I'd rather see you put money and time into something more workable.