House on parents' property - inheritance problems?

Well, he's afraid of losing control, that's clear.

Older people often do. How about a lifelong, unfounded right of reclaim for your parents?
Although in case of the (hopefully not occurring) reclaim, notary / land registry fees would be incurred, your father would have the "power" over "his" properties on paper.

So I would find an unfounded right of repayment too far-reaching again. It is supposed to be a fair solution that brings security to both sides. But first we have to obtain sound tax advice, and that may take some time, since my father neither likes emails nor conference calls, all of that overwhelms him. For him, only the personally spoken word counts, which is currently difficult.

... and on the other hand a solution where all real estate ownership is divided equally between him, his wife (my mother), and me.

To me as an outsider, this solution sounds fair (assuming that he does not want to assign you the house that you built and paid for yourself), provided that, as a balance, all the forestry and agricultural land you mentioned in another post are also included, so it concerns the total property. You would then not own anything alone and would have no sole authority of disposal, but at least more than now.

I can also imagine that if you are virtually an "equal contracting party" with your parents and this is documented in writing in all the paperwork, your parents might perhaps perceive you somewhat more than now as an independent, legally competent adult and not just as a "child." In addition, from time to time there may be decisions to be made, bills to pay, all "adult stuff."

Ultimately, the goal is to pay as little inheritance tax as possible. I could imagine that the difference between the best and the worst solution is about 100,000 EUR. And that alone is worth spending a bit more time thinking...

You definitely have to do something. Are you familiar with the statutory inheritance rules? That means if there is no will and you as an only child have not been disinherited, and a parent dies, the surviving parent receives 50% and the children (that is you) receive 50% of everything. (your statutory compulsory portion)

That is, if there is no will

From a control freak, I expect a will that is already yellowed