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Here are a couple formulas to play with. The fixed output/on-off boiler or energy source vs the modulation.

that would be tough to calculate system volume on!
fill it up with a water meter connected to the fill valve might be the only way to get a close number?

But I don’t know of any cleaners that would dissolve rust and scale to flush it out

you would need some very high gpm flow to get 5 fps flow velocity in a 6” pipe. That is what it takes to get solids moving along

This company purges large systems like that, I met them at a IGSHP show years ago.

Their purge pumps start at 5 hp and go up to hundreds of hp!

some systems get designed with buffer tanks to maximize efficiency and reduce cycling. Solid fueled boilers, large chillers are examples.

More and more we see heating and cooling equipment that can modulate, which helps reduce the buffer capacity required. Pellet and cordwood boilers now have some modulating capacity, so the buffer tank sizing has gotten smaller

There are always trade-offs. Large pressurized, insulated tanks are $$. Heat loss is a concern, space requirements also.

A buffer is an option for oversized boilers also, is the cost going to off set the poor efficiency, or extend the boilers life those are some of the decisions.

Micro and multi zoned systems with non modulating boilers are often a good match for a buffer tank.

Gravity systems with cast radiators had the buffer built into the distribution system. The boilers mass and large water content also are part of the buffer

The perfect hydronic boiler could modulate from no load to 100% load, think of a variable speed drill motor , now that would be ideal

Transfer the oil to the temporary tank and connect to the existing oil line to get the burner(s) running.

Install new oil tank with new oil line, filter, OSV, etc. to the burner. Plug the end of the oil line at the burner, and close valves.

Fill the new tank while someone is inside at the tank to observe there are no leaks during delivery.

When the temporary tank runs dry, call the service provider and they'll come to connect to the new tank. Replace the nozzle and strainer. Prime and start. Combustion test. Done.

it is not always the case that old heat emitters need high temperature supply.

Certainly not the entire heating season , if at all. Running some load numbers is the only way to know for sure

I have run cast radiators it 120f and you still feel the warmth radiating off them

Any time the iron is above ambient temperature it is giving off heat

Don’t pump it over. Its waste oil now. It’s right in the instructions. If your contractor wants to ignore it, you need a new contractor.

No amount of filtering will make that oil ok. Only a fuel polishing machine would work.

It’s only about 60 gallons, let them take it to someone who has a waste oil heater. Or like the others said, use it in the existing tank until it gets down to about an 1/8.

I run two fire tube boilers and have a box of tapered wooden plugs for just that reason. Haven't had to use them yet