I am now using oil for heating, in the last house it was mains gas, many around here have LPG gas, I think because gas boilers are cheaper, and the tanks often installed by the supplier.
I had expected a massive increase in cost going to oil, but in fact, in spite of being a much larger house, costs less than the last house. This may be down to control, as when we moved in, the central heating was in a mess, and previous owners it seems used the open fire, mainly burning wood.
I was rather surprised when we got someone to alter the central heating plumbing, for them to admit they could not do the electrics, did not worry me, but could see how someone who was not an electrician would have had problems getting the central heating to work.
I made some errors, type of thermostat for example, but the old owners to get heating to work, had to go outside, down some steps, and plug in the pump, and there was a base unit for the thermostat, but no thermostat, so selling a house with a heating system which is well under par, was likely why the house seemed cheap.
Likely the low bills are down to using programmable TRV heads, and only heating rooms as and when required, but had we asked for fuel bills they would have likely been very low, as it seems unlikely the central heating was used much, so they would be low.
We now have a split tariff with low overnight charges for electric, and we have seen where hot water is stored, this system is very expensive to install,

but my brother-in-law had it in his last house, and the massive storage tanks, I would guess around 200 gallons, did allow use of off-peak electric to heat the house, the storage tank was in fact two tanks, on a reinforced floor to take the weight, his solar was PV only, which heated immersion heaters, he had LPG and a wood burner, and his heating bills were very low, but when he moved to install that system other than when first built, just cost too much.
Again, if he had been asked for the bills, he spent so long with his daughters in Germany, the bill would not have told one the true cost to run it.
If there is room for an LPG tank, then I would make an enquiry on how much to install LPG. Use that as worse case scenario, to get the heating sorted, but electric heating can work, however it would seem there is likely a problem with the electric supply.
I also have a 60 amp supply, I look at my use, and highest use is 00:30 to 03:00 when the off-peak charges my batteries, and I often run things like dishwasher, washing machine, tumble drier and immersion heater. But during the day, the highest use is when having a shower, around the 5 kW used as the inverter can only supply 5 kW, so 8 kW shower is over what the inverter can supply. But the back-ground use is around 400 watt, with spikes when we boil a kettle or cook, so from 05:30 we rarely see any power used from the grid. So not cut and dried that 60 amps is not enough.