In what order does sqllogship.exe process groups of log files? In what order does sqllogship.exe processes groups of log files based solely on filename order or does it does it do it based on file timestamp primary sort then filename secondary sort?

It appears to handles things in filename order when all log files have the same timestamp.
It appears to handles things in filename order 


Yes and no. Yes the files are sorted in filename order which generally happens to be the same as the restore order, thus it looks like it goes in order of filename. No, because the files may be tested to see if they contain the log records for the next restore, which means their name could be slightly different and still process. Note that the filename sort is case insensitive and that filenames do matter.