High Voltage Battery Only with 240v Inverter? What's the highest efficiency possible?

Hi Mike, I appreciate the concern. My knowledge isn't the best on this, mostly because no one has ever documented the results of a use-case like this before (bypassing a mini-split rectifier in order to run the motor inverter directly from high voltage DC). I work on high voltage electric car batteries all day. I use lineman gloves and a face shield with a clean indoor workspace. I have an extreme respect for its ability to toast me in a split second.

I get that it is unnerving when I'm not solid on some more basic electronics theory, but I am experienced in how to avoid touching / shorting / energizing what I'm not supposed to. I am confident I can run some leads while the heat pump is powered down, in a way that it can be safely measured while energized.

So, common rectifiers are in the >95% efficiency range. Four arranged are commonly called a Bridge Rectifier. You need to look up in the spec sheet, your current and voltage you expect to be operating at, and record the Forward Voltage Drop ( Vf ) for that condition. That Voltage x Amps gives you the wattage dissipation you must provide for . Most Bridges have a square case with a mounting hole in the middle, to bolt it to a heat sink with a dab of thermal grease. I like to use a heat sink rated for 2x the expected dissipation, which may let you get away with out a cooling fan.
If you require filter caps, they should have a pre-charge circuit to prevent the initial charge surge from violating the peak current of the diodes. A fuse on line voltage caps is also a good idea, along with a bleeder resistor.