I'm pretty sure the barrier to the lead-gold mass parity is that due to nuclear stuff they're gonna not trade equal proton/neutron count and while of you flip the ratio you are merely dealing with an energy deficit/excess incurred as you're rearranging the protons and neutrons to transmute between gold and lead which by e=mc² is equivalent to mass... You're gonna run head first into the problem that we with our current proven understanding of atomic nucleus quantum physics, expect the energy excess to need to be turned into an equal split of matter *and antimatter*, which will foul your plans.
We're suspecting there to be some symmetry breakage to explain why we don't really see any globs of antimatter with our telescopes (at least none that show any evidence of being antimatter), but so far no (real) luck.
As for the "0.13€ vs. 1€": you're not gonna get much solar yield in peak winter at least in Central Europe, especially it's gonna be that your PV is going to charge <100hour electricity storage when the sun shows up on those winter days and the heat pump (at least the part that spends a little electricity to lift a lot of heat energy from outside temps to indoor temps) runs approximately continuously.
You might have some kind of e.g. water/water heat pump with salted (not table salt though) water deliberately thawing during daytime (by turning on the circulation between it and outside air) to freeze at much warmer than night air temperatures to buffer those "only mildly freezing" temperatures to improve the efficiency (and at that point, likely also the thermal output power) of the heat pump.
The radiators inside and potential fans for them would also go up in flow to make up for the increased losses through the walls/window-glass.
A big reason why at least in e.g. Germany heat pumps are not at all irrelevant vs. electric resistance "space heaters" is that they're also very efficient at handling spring/autumn (lower thermal delta to lift against; referencing to a resistance heater for scale/reference purposes but clearly not expecting that to be a benchmark) while easily offering summer cooling (with relatively minor incremental complexity).
I don't really know how inherently expensive it is to keep around at least for parts of each city, but existing natural gas central heating boilers are very useful to not just trash before they're broken just because one uogrades to a heat pump, specifically because they are already there (sunk cost/little scrap value) and have basically zero issue delivering extremely spiky power during unannounced winter days (well, takes maybe a day of notice to actually get crew in to the storage&distribution facilities, but weather forecasts easily cope).
Sure, it's not _efficient,_ but we could just divert some synthetic methane during summer to refill the caverns: we kinda want that (at least for hydrogen but methane works too at least for storage) anyways for chemical synthesis factories if we're not just gonna feed them crude oil/natural gas, so other than that chemical factories probably/largely prefer direct hydrogen, continuing to use our existing seasonal storage even if it's not getting refilled from NordStream2 but from local summer-only electrolysis plants and with more hydrogen than methane where the geology allows, seems to me just frugal dealings with nature (reduce, Reuse, recycle).