This I wasn't quite aware of. Thanks for the correction.
> But it's theoretically possible to burn hydrocarbons and turn the CO2 into coal and leave it like that with a net energy gain
This would be a game-changer! Though "theoretically" is pulling a bit of weight here...
> We should get rid of coal first, as it's irredeemable in this regard and methane second, as it's a greenhouse gas which tends to leak,
I also agree with your list. Burning stuff for grid energy should stop ASAP. Liquid fuel for transport is, however, the most difficult and probably the last to be replaced. It's to the point that generating green liquid fuels (that don't use fossil sources of carbon) is still actively researched and used, as air travel or shipping may never become feasible on green energy sources.