Yep.
When it comes to orientation and positioning of the compressor cover and actuator during assembly, they do not have an actual jig or motor to use to align everything. The builders have a general guideline to follow that gets the compressor cover orientation close. This is the same for all Buick 3 bolt turbos that get an actuator with the order. When you figure two guys are averaging 100-150 turbos a week and out of those maybe 20 are Buick 3 bolts, on top of that out of those 20 maybe 5-6 get an actuator with them, you can see some slight differences in the clocking. I can say tho, that those guys in the shop bust tail and are very good at what they do. All of them. Matt, Jim, Steve, Dan, Tony, everyone back there kicks butt.
When I took my 6031RE out of the box, and installed it, I too had to reclock the compressor cover down slightly. This turbo is physically identical in dimensions to your 6776RE. Only real differences are the wheels. And yes, your actuator that you show is identical to the one I have and it works flawlessly.
http://i78.photobucket.com/albums/j96/Patricks_cars/87 Turbo T/DSC00481.jpg
I re-clocked my cover, being careful not to rotate the cover too fast or use too much force and re-tightened all the backing plate bolts hand tight in a criss cross fashion. Reason being is, there is an O-ring that helps to seal the compressor cover to the backing plate. And if you use to much force there is a chance that you can tear it. They do put a dab of oil on the o-ring during assembly so you should be ok. You should be good to go from there.
The only other issue I had was this,
The special oil feed line sticks up too high. It keeps the heat shield from sliding down far enough to be bolted up to the question mark bracket. You either have to cut/notch your heat shield to clear the oil line, or create a different oil feed line setup using different fittings.
Hope this helps, and you are going to love that turbo.
Sweet looking motor too.
Patrick