I think your nearest point of navigable waterway would probably be Tulsa, Ok. The MeClellan-Kerr Waterway I believe begins/ends in Tulsa. It is the Arkansas River and not part of the Great Loop itself but it will get you to the Mississippi, which is part of the loop. The ride through Arkansas is pretty and several locks and dams. Tulsa is porbably around 1,750 miles from SF Bay.
I believe the next closest point would be Houston/Galveston Texas area which is near the ICW. You can take it south to Mex. or north and east to the loop. Some people consider the Texas coast as part of the loop because of the ICW, but it is not the actual loop itself. This will probably be about 2,000 miles from your area.
There is a point about 150 miles or so south of St.Louis, Mo. where you can get off the Mississippi and swing over to Ky, Tenn, Ms and Alabama and get to the Gulf to complete the loop. This is the scenic route and officially part of the loop.
We are an older couple, 65 and 71. and will probably do the loop in a few years from now.
Cruising the Eastern U.S. Inland Waterways and Gulf Coast. Presently on the ICW in Louisiana and heading Back to Texas.