I wonder why one is immediately insolvent. Why not just rent out the house "simply" and, in the worst case, pay some difference towards the financing?
I would also like to pay off more, no question, but the risk you mentioned unfortunately goes against the realistic plan that in the first years less can be paid, because possibly. offspring/part-time work, something done to the house, and only later after 10,15 years the rate can be increased again... unfortunately that is unfavorably counteracting.
I am currently calculating a lot, e.g. 20y interest approx. 2.31%, then follow-up interest assumption 3.5%. You are already above that compared to the home savings contract construct concerning the total costs and you have no interest rate security.
The home savings contract construct doesn't seem to be really bad...