I just had a play around with this, seems to work well even if it is a very simple example. Here's what I did.
1. Download
http://www.ashesofthefallen.net/drumedit2.zip and open the project. We can see that the project has already been split at the transients (TAB to Transient then 'S' to split. Observe that the snare hits are not bang on the grid.
2. CTRL-A (to select all), right click over the items and select 'Item Processing -> Quantize Item positions to grid'
3. Check 'Shorten earlier...' and set to '0'.
4. Observe how the snare hits now align to the grid, but has spaces between them.
5. Ensure that all clips are selected and right click over the items and select 'Item Processing -> Quantize Item positions to grid'
6. Check 'Extend starts...' and set to '10'.
7. Check 'Shorten earlier...' and set to '10'. (Chances are, this box was already checked, just change the value to 10).
8. To consolidate, ensure that all clips are selected, right click over the items and select 'Glue selected items'.
If I've missed out on anything here, please do feel free to correct me.
Now to try this on multiple tracks with alternating tempos and time sigs...
Edit: Just saw new posts while I was typing this - I'll download the .rar file and have a play around with it!