How to avoid cascading resizes when resizing hash tables?
You ask how to avoid cascading rehashes but you already gave the answer in your post. You keep the probability that bad events occur small. 

Since you mention cuckoo hashing. The probability that you get a long probing sequence is $O(1/n^2)$. So if you rehash, you are inserting $n$ elements from scratch. The probability that the rehash is not successful is then $O(1/n)$, so with very high probability you are successful. In expectation you need only a constant number of tries. If you observe that you have problems with rehashing, then you should increase your table size and modify your load factor. Alternatively you can select a better family of hash functions.