Matching delayed signals
This may be a good candidate for a two step approach: 

Step 1 would be a pretty coarse running cross correlation with a threshold detector to identify what parts in the signals are matching. 

Step 2 would than determined the actual delay. There are various ways to get sub sample resolution:


Upsample to desired resolution and then cross correlate
Short term fourier transform and match a linear phase difference with a weighted least squares approach
Delayed lock loop with a fractional delay filter
Match the the two signals in with an adaptive filter. Then calculate the fourier transform of the filter impulse response and calculate the delay through a linear phase match