Best Of
Re: Replacing an old/inefficient oil burner with...an oil burner (?) Or...?
With high heating costs and\or comfort issues I like to start with the question: how much “pain” does it cause you?
$5,000 to heat your home for a single winter would be very painful for most of the folks I work for, and it’s painful to hear that you’re having to spend as much to heat your home.
In my own home, the combination of “going to be here for a long time” and a lot of pain from high energy bills led to a willingness to spend a lot of money to both dramatically increase our comfort and reduce home energy costs.
Big picture: I’d find the best guy\gal in my area for the job, and I’d buy the best piece of equipment he is recommending for the job.
If I were in your shoes right now: I would line up the site visit with the heating contractor. Before the site visit, I would determine where I could seal up and insulate cost-effectively, and then I would have the contractor size the equipment to the new load. I would run the numbers, based on the contractor’s chosen equipment, and decide whether a new boiler makes sense on the numbers alone.
If a new boiler did not make sense on the numbers alone, then I would look at how the air sealing and insulation measures stacked up on paper.
My bet is that your best path is to spend a chunk on air sealing and insulation measures, and another chunk on a mid-efficiency boiler that will reliably make it to the 20-year mark.
FYI: The average job I take on significantly addresses envelope issues as a path to cost-effective heating solutions to high home energy costs.
Re: Best Solution for Connecting Copper to Iron Boiler
just use a copper adapter. it is all crusty because it is leaking, not because it is iron to copper.
if it wasn't an installation issue then you might want to be concerned about the system getting a lot of makeup water or possibly an issue with the electrical system.
the leak is above your picture somewhere, wherever that crusty trail starts.

Re: Replacing an old/inefficient oil burner with...an oil burner (?) Or...?
It is unlikely that replacing the boiler with any option would save enough to pay back in 15-18 years.
It is worth figuring out if the system is designed correctly and if the burner is set up right but beyond things like that, changing equipment is likely to cost more than you will save.
If you are also making dhw with the boiler, that could potentially be made to cut standby losses significantly for relatively little cost.

Re: Burnham Heat Exchange Leak - RV5NSL-L2 Boiler Seal to slow and plan for replacement?
It looks like you will easily make it to spring only another 4-6 weeks.
I would avoid sealer unless the leak gets much worse.
Re: Burnham Heat Exchange Leak - RV5NSL-L2 Boiler Seal to slow and plan for replacement?
@New England SteamWorks or @Charlie from wmass
And don't buy another Burnham. There failure rate in MA & Rhode Island is excessive. Especially with a water boiler you should have got more than 20 years out of it.
Re: Packing Heat
Perfect is the enemy of good enough. The goal isn't to use zero grid but minimize it since it is expensive. With your costly power, even an oversized zero export setup where you waste some solar has a good ROI. With a bit of home automation, you can set the heat pump to run when you have extra PV and try to coast through peaks.
You can also install an oversized resistance tank with a diversion controller to capture the excess PV. These are very common item overseas but are now some available here as well.
Some car chargers also have the option to monitor load and can throttle back if the sun is not shining.

Oil Burner Tools
To All the Old timers who worked on oil burners what are some old tools that you have or had that you used specifically for troubleshooting oil burners. I.E: Osv tool or oil line watcher, on watch or even inline gauges. I work on quite a bit of oil burners in commercial space it’s crazy how the old stuff seems to work the best.