You Sir, are an official Jammy Barsteward!
Nice one!!
I have a Record 073, a No10, a 778 and a router slightly more patinated (rusty) than yours...so...here's some experience:
"what does a shoulder plane do that a no 78 couldn't?"
My Record 074 is a tonne weight. That makes the trimming of tenon shoulders really easy, as once started, the momentum and gravitas of the thing tend to hold it steady through the cut and even knots get trimmed snoothly (but you NEED a sharp blade). Helps a lot that they are bevel up and shallow angle. The sides on mine are mercifully square to the sole and I find running the side on a properly cut tennon face ensures a right angle to the shoulder face.
Your 78 cannot trim tenon shoulders in this fashion, and, even though it excels in cutting rebates to depth, it is debatable if one could hold it properly across the small breadth of a tenon to achieve an even tenon. It is also across the grain and your router cutter will be more efficient here.
The router you have can be easily adapted to cut tenon faces, see reference to Bob Wearing's 'router foot' arrangement, long used in the past before power in workshops became common. The 'foot' can be attached via the fence holes in the sole.
Staying with the fence, I personally found it got me out of a cople of snags, particularly with a rounded table-top edge, just had to mind the grain direction VERY carefully.
The depth guage IS useful, but as someone said, the router just stops cutting at the set depth.
My 778 and your 78 can cut rebates WITH the grain, even up to within a few mm of the end of a stopped rebate. My No10 cannot, as the sole is far too long in front of the blade.
HTH, Sam.