Hello,
the additional cost is really quite high. Or is it perhaps that the gas boiler is still calculated with regular radiators and the heat pump includes an "upgrade" to underfloor heating?
But your calculation is basically quite correct. If you calculate soberly, the heat pump is still at a disadvantage at the moment. How this will develop in the long term, nobody can say.
We therefore also decided on gas. But definitely design the underfloor heating so that you can install a heat pump later. In other words, the pipe spacing must be small enough to allow for low flow temperatures. The gas heating won't last forever; in about 20 years you'll have to replace it and then, with high probability, you won't be allowed to install a gas heating system anymore.
Regarding the 20 kW peak power. You don't need that for heating, but for hot water production. And with 4 kids, you'll need that! With the heat pump, the 300-liter hot water tank would be borderline. If someday 6 people want to shower in the morning, the last person will only get cold water.
The gas heating can practically reheat the water on demand with 20 kW.
Best regards,
Andreas