I ran into something similar with a flip that had an oil burner, and the oil soot was circulating in the house due to a bad burner.

If the heat is radiators from a boiler, you have to separate the supply piping and return piping for each unit, then you need the extra boilers as well; you might be able to re-gun the oil boiler with something like a Midco Economite to save some money on a boiler, assuming existing boiler is in good condition and not too oversized for the biggest rental unit.One thing to point out is that you will now have multiple burners.

After our helpful movers and my cleaning lady left, I attempted to light all of the electric stove burners (stove was harvest gold, most likely from the 1970's). 

Ovens and multiple burners running together eat up a lot of power, You don't want that power running through a cord with insulation flaking off and a couple of nicks in it from routinely moving the range out of place to clean behind it.I realize that appliances costs money to replace.

But more often than not, investors who involve a buyer's broker get put on the back burner and are used as a last resort for the reasons I've mentioned above. 

My flip house got kicked to the back burner quick.

However, a wayne conversion burner and a guy who understands how to change the burners will accomplish your task.

Most people with school aged children put house hunting on the back burner during these months.

Putting the tax implications on the back burner...What is the legal exposure here? 

I'd put this one in your "on the back burner" bucket.