I would probably lease the property to the neighbor for the relevant period. Firstly for a fixed period to set an end date; secondly, to elegantly transfer liability for actions of third parties (and their accident risks). The lease payment can be symbolic.
I would also get it in writing (not orally) that you are allowed to store your crane on his property
People, one can also overdo it. The OP has probably already spoken with the neighbor several times and can best assess him himself. If a new neighbor comes to me and wants to place his crane on my property for 4 weeks (normal construction time for the shell), why not? With lease agreements or such nonsensical demands, you already ruin the neighborhood in advance.
@OP Let the neighbor maybe place the crane exactly where your driveway will be later or where you want to place the crane yourself -> compacted mineral concrete already in place. With a case of beer, that should settle things between you
With stone made of stone and with a gable roof, the neighbors won’t be finished in 3-4 months. Especially since bad weather could also come now.
What should take that long? A shell without a basement is built in 3-4 weeks. Then another week for the roof and then the crane can go away. Ours stood, I think, 10 weeks (with basement), but was not used for the last 2.5 weeks already.