Not a good recomendation to conduct the first service on your own. I will give you the "What Ifs"
IF you do the service, and IF you experience any trouble with the bike that could be connected to not having a Triumph tech doing the service, there is a chance that waranty may have issues with covering a repair.
The first service is the most important one because the techs look for safety concerns. Loose or missing stuff that sort of thing.
(Here come the IFS again) IF you do your own service, and IF you miss anything (from a safety perspective) and IF (God Forbid) somnething happens, well, you know the rest of that issue.
IMHO, the $$ spent on the first service is well worth protection it provides in case of future issues. Think of it as an insurance thing. As for the other services, they are more descretionary. But after 6000 miles, the odds of anything being loose from the factory are almost nill.
JMHO