Can high-entropy data be reconstructed from plaintext XORs in CTR nonce reuse?
A block cipher in CTR mode is just a stream cipher.  You have a stream of bits that are indistinguishable from random (assuming good things about the block cipher) and you xor that stream with your plaintext.

What happens when you reuse the stream?  It allows an attack to take their knowledge of one plaintext and use that knowledge to expose information about the other plaintext.  If you encrypt all-zeros as the plaintext (or any message entirely known by the attacker) then the attacker knows the stream and can perfectly decrypt the second message, no matter what that message is.  If, for the re-used portion of the stream, you encrypt two different perfectly random and secret bitstrings then the attacker will learn the relation between the bitstrings, $M_1 \oplus M_2$ but nothing more.