Looking for encryption algorithm not subject to known-plaintext attack with IV reuse
Well, your requirements sound pretty much like standard disk encryption ones.

Assuming you can assign IDs (0,1,2...) to each 4kiB sector implicitely.In this case you could simply use XTS-mode of encryption using AES.
You'd then iterate through the 4kiB block using the inner counter and iterate through all sectors using the outer counter.

This should give you best possible security, as the same plaintexts are mapped to different ciphertexts (because of the counters) and there's no keystream to break.

I hope this is a solution to your problem.