The thing with persuasion was of course a joke. Still, it would somehow be nice if, in a joint construction project, not only one side had to make compromises.
Your neighbors have not promised you shared suffering before any altar!
The basement is non-negotiable for us.
Absolutely. "If the lottery fairy doesn’t draw my numbers, I’ll die immediately" – such a fatalistic attitude is unhealthy and will never have the strength to force supposed luck. By the way, you haven’t commented on the slope location yet.
Would a partial basement perhaps be possible that leaves some distance to the property boundary? I don’t know how much distance would be necessary, 1-2 meters? Would that then be less complicated? Then the basement would not adjoin the neighbors’ property, but would be completely underneath our house.
I deliberately only mentioned the brief point without a long explanation because a partial basement is possible but uneconomical. The distance must also take into account the slope of the excavation pit, so 2m would be roughly the lower limit (and your staircase would thereby be fixed to the side away from the neighbor, although it would actually be considerably cheaper on the “shared” wall side). This Pyrrhic victory is not really necessary. Rent space in a self-storage center if you still need time for sorting flea market / recycling yard. A basement for junk capacity is by no means the only option.
I would rather try to raise the roof pitch, if possible. That doesn’t make as big a financial difference as building a basement additionally. If necessary, I would offer to share the additional costs.
If a longer house length is allowed, that would be easier, then you could abandon profile equality in the additional length. But I do not really see this as necessary here.