I have no experience with this type of conversion, but I will give you my thoughts. It is cheaper to just change the burner, but you give up efficiency. I can recommend the Carrier dealer I use if you are in or near Mercer county. They are currently swamped with work, so you are better off if you wait until the fall. Whatever you do, I recommend not using AJ Perri.

I have no experience with this either - but I do have experience with gas furnaces. I can't imagine a conversion that would be the right answer.

New gas furnaces are easily 92-95% with condensing secondary heat exchangers, outside air intake, venting through PVC and ECM blower motors. All of those things are great to have. Venting through PVC solves venting issues (lining a masonry chimney, for example). Outside air intake reduces air infiltration. ECM blower motors ramp up slowly and use less electricity both in the winter and in the summer w/AC.

You will give up a lot trying to do a conversion - and I can't imagine you would save much money.

We converted a System 2000 boiler from oil to gas without a problem. We were told though, that the two hot air furnaces in a two unit building could not be converted. It would require new furnaces. And we would have to do a new metal chimney liner and do them at the same time. You can’t run oil and gas in the same chimney flue.

You may have converted it "without a problem" but note mike_home's comment, "It is cheaper to just change the burner, but you give up efficiency.". Also note you seem to be describing a boiler and the question is about a furnace. Is that similar or different as to the effect of the change, not something most people would know.