Hi Tom,
I have been up my friend's H376 stick multiple times for annual inspections and service. Going aloft must be done as safely as possible, and when done so, can be a rewarding experience. Take a camera for "sightseeing photos" after the work is done!
1. I don't think anyone mentioned--I always felt there was a small chance of toppling out of the chair. So, I tied ONLY the primary to the chair. I tied the backup to "me". More specifically, I bought an inexpensive rock climbing harness and wore it. Before I had the harness, I used a deck safety harness. The deck harness was NOT suited to the job. However, it can arrest a very short fall (so keep safety line slack-free) and prevented serious injury.
2. On a fractional rig, some halyards cannot serve as backup for the last 10 feet or so. On the 376, the spin halyard exits the mast 10' short of the top. Make sure your primary and secondary can BOTH protect you at the top.
3. Some additional tips
Yes, help the grinders. There were fat shrouds all over the place on a 376 rig that I could grab and pull (uppers, intermediates, lowers--oh my). They were easier to grab than the mast. Do so to ease lowering also.
Electric grinding assistance is OK, but it complicates things. I wouldn't go out and buy anything, but I'm old-fashioned. You should have multiple folks assisting anyways for safety. They can take turns grinding if you do not have The Hulk as crew.
Usually we used the main halyard and full diameter topping lift as some combination of primary / backup. When one was not available, then we used one of those as the primary, and the spin halyard as a backup.
In the above situation (AND THIS IS A HANDY TIP FOR A LOT OF SCENARIOS)-- I brought 20' of line with me. When the spinnaker halyard no longer protected, I tied a prusik knot around the mast, and then to my harness. This knot can be shimmied up the mast a foot at a time as you ascend.
+1 to justsomeguy for double figure eight suggestion. Bowline works also but I feel like double eight weakens line less (all knots reduce strength of your rig).
Learn the prusik. Not that you will use it for your project, but, it's easy and handy. It can also be used at the masthead to fashion a step to achieve a higher working platform than a halyard allows.
+1 nveater--do NOT use shackles.
I hear concerns about reaching around to front of mast from a position behind. In my experience with Hunter mastheads, I could kind of roll around to the front, or at least lean and look to the front, to see it. Then, I could disconnect anemometer by feel / semi-blind. Then swing around again and look--there are often little notches in the hardware that have to align. That said, each wind rig might be installed differently. Do a good inspection while you are up there and maybe change nav lights while you are at it.