Couple of things that comes to mind are...
Are you using the latest OS version for your Triton?
The Triton Classic had some issues with Midi in early versions of it's OS and the Trition Studio had a few werid behaviour issues with midi too unless you updated it....
Search google for Korg Triton update to find links to the various updates depending on what version of the trition you have....
Finally the 11.1 driver for the Digi are not fully compatible with 10.9.2.... Several people I have spoken to, have reported various issues including weird midi behavour at times.. with that interface using those drivers... with 10.9.2.. They seem to work better with 10.9.1 but even then there were still some problems I gather...
I also noted that Digi may have now updated the notes for 11.1 with the following comment...
Mac OS X 10.9, 10.9.1 Mavericks support only
I think it just used to say Mavericks support only in the past, and not specific versions.. but I could be wrong....
Personally, as I have a Triton Classic here working without issue with my Motu Ultralite and LPX.... I suspect its your audio/midi interface and drivers that are likely to be the cause of your problems.. given you have done all the standard other 'fixes' for such issues without success.