If you set up the boiler to cold-start, and use an "indirect" hot water heater operated as a separate zone for the boiler, you'll usually get better net efficiency, and higher summertime water heating efficiency than with an interal coil. This is not the simplest thing to measure, but this has been looked at fairly carefully by the folks at the
Brookhaven Nat'l Labs.
If you then run the boiler & indirect with a heat-purging boiler control like the Intellicon 3250HW+ or similar your standby losses plummet, and your water heating efficiency rises- approaching that of system #3 (see table 2 in that linked document.)
The problem with embedded coils is that you have to maintain the boiler at a higher temperature at idle in order to get reasonable hot water heating performance out of it- typically north of 150F, often north of 160F at the low-limit. You can experiment with just how low you can take the low-limit before you're not getting enough hot water, but don't take it lower than 140F, which can result in corrosive condensation on the heat exchangers in the boiler and in the flue if you run it much lower temp than 140F on a regular basis. (Got a make and model # on that boiler?)
But whether installing an indirect hot water heater and smarter controls for the boiler is the best investment remains to be seen. If your house has a reasonably open floor plan you might get better overall return heating most or all of your house with ductless mini-split heat pumps, at least during the shoulder seasons, and save a lot more oil than an indirect would. Of that 1000 gallons/year only about 150-200 gallons is likely to be for hot water heating- the rest is space heating, and even a 1-ton mini-split can probably handle more than half the space heating load, at an operating cost about half that of heating with oil at recent prices. For many homes a mini-split or two can be
the solution to the $4/gallon heating oil. See
this recently published policy piece on relative costs and environmental impacts of different alternatives to heating with oil. High-efficiency heat pumps are right in there with condensing gas on operating cost, cheaper than pellet boilers, etc.- see figure 2 on page 6.
Like wood stoves and pellet stoves, it's point-source heating, so doored-off rooms on the other end of the house will run colder, but far more convenient to use, and they also run as high-efficiency air-conditioning in the summer.