So,
is this what you would pay for gas in your neighborhood? For heating customers it looks like the delivery & service charges are ~$85 for the first 50 therms (which would be most months if heating domestic hot water with gas for a family of 4) plus $0.50 cents per therm for the gas itself. For a low heating shoulder season month that uses 50 therms that's 50 x $0.50 = $25 for the gas, $85 for the delivery, $110 total for 50 therms, or ($110/50=) $2.20/therm.
Using an 82% efficiency gas retrofit burner that delivers a net 0.82 x 100KBTU/therm= 82,000 BTU per therm for ( x 50 =) 4.1 million BTU (MMBTU) net heat into the system for $110, so it's a fairly steep $110/4.1=
$26.82/MMBTU or more for low usage months.
For a higher use midwinter months you might be using 300 therms. The first 50 costs $110, but the other 250 therms is costs only $0.29 for delivery, $0.44 for the gas for $0.73/therm, so you'd be looking at a total bill of $110 + (250th x $0.73/th)= ~$293 . That's an average of only $293/300= $0.98/therm, which is less than half the average cost per therm for a low usage month. Normalizing to net $/MMBTU that's 300 therms x 100,000 BTU/therm x 0.82 efficiency = 24.6 MMBTU for $293, or ($293/24.6 MMBTU =)
$11.91/MMBTU during the ~3 heaviest heating months (probably ~2/3 the annual usage or more.)
Oil burned at 88% efficiency in a Sys-2K delivers a net (0.88 x 138,000 BTU/gallon =) 121,440 BTU/gallon, so it's (1,000,000/121,440 =) 8.23 gallons/MMBTU. At the previously stated contract price of $2.33/gallon that would be
$19.18 MMBTU, with all months being roughly the same cost.
If you're spending a couple grand per year that's $2000/$2.33= 858 gallons/year or (0.82 x 138,000 x 858 gallons =) 97.1 MMBTU/annum. Something like 3/4 of that during the coldest three months, or ~73 MMBTU, which costs (73 MMBTU x $19.18/MMBTU= ) ~$1400.
To deliver the same amount of heat with gas during that season costs only (73 MMBTU x $11.91/MMBTU=) $870, a $530 savings for the heating season.
Assuming
all of the other (97 MMBTU - 73MMBTU = ) 24 MMBTU per year is at the higher $26.82/MMBTU low monthly usage price point the remainder of the year costs another (24 MMBTU x $26.82/MMBTU = ) ~$644.
But with oil the rest of the year would only cost (24 MMBTU x $19.18/MMBTU= ) $460, which is $184 less than with gas.
The net annual savings with gas vs. oil at those prices would be ($530 - $184 =) ~$350/year.
Assuming the Sys- 2K has another 10 years of life in it (which is all but assured) the remaining lifecycle savings would still be only $3500, if 15 years (there's still pretty good chance it'll go that long) it's about a 5 grand savings. But since the gas plumbing is already installed you'd then be able to replace the system with an even higher efficiency condensing boiler (if that's still even legal in 15 years, depending on state & federal policy changes) without a lot of extra expense. But even at the end of 15 years it will not have "paid back" even in simple terms if the conversion cost is $9-10K and just replacing the tank is $2k -$3.7K.
Of course this all presumes that pricing per MMBTU for gas relative to oil will always be in lock step, which it sort-of is most of the time, but not always.
If the long term goal for this house is to get off fossil fuels it's better to save the conversion money up front, and in the nearer term spend the difference on fixing the air leakage & insulation deficiencies of the house to increase the
house efficiency & comfort, which would also lower the annual operating cost. Then when either the central air or boiler craps out (one or the other probably will fail to the point of not being worth fixing within 15 years), replace the AC with a right-sized heat pump solution.
If local, state & federal policy makers make it worthwhile with big subsidy or carbon tax incentives it may become reasonable to retire the existing heating & cooling systems even before end of the anticipated service life, but no matter how you're heating and cooling the place, fixing up the thermal performance of the HOUSE is the necessary prerequisite for making the place truly comfortable. Even with the oversized systems comfort will increase with a tighter, better insulated house, but when the systems are replaced with right-sized equipment for the (now lower) design loads the comfort levels would then soar.