Well I think I found him, but am not 100% sure!
Glad you found a possible candidate, even if not a perfect match. Riggs and Grigg are rather different, but 'mis-spelt' names do occur in the ships' musters/paybooks. It seems they were simply copied from one book to the next, until someone took the trouble to make a correction. I don't see why the yard paybooks should be any different.
If he was working on a supply boat aged 40 I guess this does make it likely he served in the Navy before this.
I'm not entirely sure that assumption is well-founded. He might have been working in a clerical post elsewhere for the Admiralty, or for another institution, rather than on active sea-service? The required skills would be different.
Is there any easy way of tracking down any Royal Navy or East India Co. service he did before 1779?
At this early date and without the name of a ship, I think not. But you might want to ask a Moderator to move this thread to the Armed Forces board, where you might get more expert help on that point? Or start a new thread on that board, linking to this one?
The only other thing I would suggest (if you haven't already tried) is the Cavendish-Bentinck estate papers at Nottingham University (Special Collections). If William Riggs' father contributed to building Bulstrode, there's just a chance there might be something there. You could try emailing the archivist for advice on that specific point? I've always found them helpful there.
http://www.rootschat.com/links/01adm/