Hah, from Belgium I can relate with the nonsensical requirements for grants and the fact that heat pump units can be hard to install in row housing.

Sounds like the rules are stupid and only written for new construction or very deep renovations. It will almost certainly be more cost-effective to do your own thing, without government help.

I haven't made the plunge yet, but a reversible mini-split is probably what you want. They're much smaller, wall-mountable units that require no change to the existing heating system (and are easily DIY'd if you can run the electrical circuit yourself). You can put one ventilation box per floor, which should cover the vast majority of your heating needs. Sure, it might not have the capacity to heat your house to 20°C when it's -5°C outside (unless your house is really well insulated), but perfect should not be the enemy of good. Not turning on the gas boiler at all on mild winter days is already a big win.

For tap water I believe there are models that have about the same dimensions as a standard water tank but with a heat pump integrated. Can't say I looked too deep into that though.