Best Of
Re: Rebuilding old radiator valves or replace?
Those old valves are much better than the new ones if you can save them.
Re: Humming to Hold Music
A lot of places are starting to use a call back option. You leave a message, and they call you back. If done right (sometimes questionable) its better, you can hang up and do something productive while waiting for the call.
Re: Looking for advice on balancing the system in my house to to help with heat and clanging
You have significant piping problems with your boiler which may restrict what you can achieve with venting.
I'll try to get you better heating on Radiator 3-1:
Try putting a slow (Hoffman) vent on 3-2 and see if that forces 3-1 to heat.
(There is no blockage in your 1-1/4" pipe. The panting vent is from bodacious condensate forming waves in the small, long runout by the fast venting. You can try increasing the pitch in that runout by lifting radiator 3-1 an inch or so…)
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Then if that helps:
I would switch the two main vents from Main #3 to Main #2.
Re: Vintage Burnham Aquastat
The old aquastat should have some markings on it telling you what the differential is. What makes you think it is short cycling? Have you checked the aquastat contacts with a voltmeter to confirm that the aquastat is what is opening to shut the burner off? Is this a 24vac system or a millivolt system or some other type of system?

Re: Near boiler piping
that’s good observation. Get good 1” insulation be aware it doesn’t heat the pipe it only slows the cooling.
Re: Heating recommendation for Jackson, WY
and consider who will be contracted to build the home, install radiant systems etc. It can challenging finding anyone with specialty knowledge required.

Re: Heating recommendation for Jackson, WY
Theoretically you should be able to handle the load with radiant floors — but that pretty well assumes that all of the floor area is available. Which it won't be. Cabinets, furniture, rugs…
Even so, the basic premise is quite sound.
However.
It is sound only if you insulate the dickens out of that slab. I'd want at least six inches if not more of insulating foam underneath it, and a good foot of foam on all perimeters..
Also, remember that floor radiant heat responds very slowly. Therefore I would also have a higher temperature loop or loops with panel radiators which can be used to bring space temperatures up when the response is needed. Use the floor to maintain base temperature — perhaps 65 or so.
Re: Boiler Running Full Tilt, Cold House
I open them all the time. They offer a cleaning tool for the older models. It's a pin type HX. They only want a water flush with the new blocks. If they're burning clean, The HX is always clean.
Their U Control is very easy. It can accept 3 different circuits. Min/max firing rate for each circuit. Min/max temperature setting for each circuit. Floor standing or wall hung. I'm not crazy about the Series 1 and 2. But with the revisions they've made through the 3, the Series 4 is a nice boiler IMO.

Re: Lennox furnace stuck in heat mode
OK light at the end of the dark tunnel. ebebratt was right red and white connected furnace on, diconnected furnace off. More importantly I swapped the thermostat and base from other side of the house and furnace is functioning as it should heat comes on demand and off when switched to off.
Ordering a new Nest thermostat
Thank you Ratio, God bless you! HVAC service call out of the budget for this retired guy.