I would like to provide you with some useful links. But I'm not familiar with the behaviour of tvheadend because I don't use it and don't have the equipment to simulate it on your behalf. I use set-top boxes/SAT receivers for live TV and therefore know the limitations associated with it.
Please understand the possibility to record multiple programmes from the same transponder (MUX) with only one tuner in use as a benefit for free. I would assume that tvheadend supports that out of the box, without special settings. It depends more on your typical TV usage if you a have a benefit of it or not.
For example:
If you have a primary place in your home, where you and your family most times join to watch TV together I would place the device with the most available tuners there. From your mentioned list the Hauppauge Dual Tuner looks like something to me, because it's mostly directly supported by the linux kernel. You are able to watch a show with the first tuner unit and can run a record in the background at the second tuner. If you have a second overlapping/simultaneous record scheduled and fortunately the additional program to record is receivable via one of the already tuned transponders (tuner1: live tv, tuner2: current running record), then this additional record is also possible. If this program is played out on a third transponder only, this 2nd record isn't possible. Thats all.
It looks to me like you could use the remaining devices (RPi with HAT, August on Windows) as a Tvheadend SAT>IP server. If you need a 3rd or 4th tuner in your typical use case, you could add these devices as network tuners in Tvheadend and have a total of 4 tuners available in one KODI instance. Several combinations of your 3 devices are possible, but to make it useful for everyday use, the remote devices should run 24/7 without interruption.
I hope this attempt to explain clarify somethings to you. 