I think I've read that 3 times now and every time I get to the fart auger part I lose my thought train.
Sounds like you'll want a bag of DPDT relays with 120 and 24V coils, a delay on timer and cycling timer. The timers are solid state and available from US manufacturers as Mr. L mentioned, or if you would like a bit more flexibility there are the chinese variants that, to me, open many possibilities for customization such as this timer:
https://www.ebay.com/itm/Inkbird-IDT-E2RH-110-240V-Digital-Twin-Timer-Relay-Time-Delay-Relay-Switch-Black/161856543726?ssPageName=STRK%3AMEBIDX%3AIT&_trksid=p2060353.m1438.l2649Without seeing all that on paper I'm only getting part of it since I'm not in the industry, but couldn't you use a chinese temp controller to close the circuit for your pumps, fans, and auxillary boiler trigger? You can switch them to NC or NO with the appropriate relay and most even have a delay on timer, some have dual relays, and most have sensor offsets which the Ranco doesn't - at least mine doesn't. ...For some reason.
I tend to overcomplicate things, but sounds like a thermocouple type temperature controller would trigger your backup system when the flue temp of your wood job gets too low.
Even the X410 unit has some pretty slick features for operating relays with its logic controlling abilities. I'm quite impressed with what it can do.
There's probably a hundered ways to do what you're trying to achieve, the tricky part as designing it simply as possible and function effectively.
Should be able to do all that. The biggest deal is the domestic hot water. On demand hot water you would have to anticipate use or go to a side arm or or secondary pump to the water heater to put it on a t-stat.
This is how I've got mine setup, taco 006 on a thermostat. Works quite well.