... as soon as I plug in ... any other AC powered effects, I get hum. An Ebtech hum eliminator cures the problem, but I'd rather not use it.
Everything is working exactly as it should.
When you plug in a.c. powered effects, your cable's shield/ground connects the chasses of the two pieces of gear together. Now ground currents have 2 choices of path to follow to get back to outlet ground: through the amp's power cord or through the effect's power cord.
The only safe solution to breaking the big ground loop just created is to isolate the ground of one piece of equipment from the other. The Ebtech does this with an isolation transformer in the path of the power cord. That's why it stops the hum.
Theoretically, you could modify one piece of gear to have a ground-lift, but that's a hassle in an amp which wasn't designed from the start to have a ground lift (the
entire power and signal circuit of the amp has to be isolated from the chassis with only one connection at a lift switch bypassed with a cap and diode or resistor).
You could also theoretically move the transformer to be in-line with one of your connecting cords (i.e., bass into splitter, 1st cord from splitter into effect, 2nd cord from splitter into transformer then 3rd cord from transformer to amp).
So the existing Ebtech is very likely the easiest solution.