Try a plunger in the shower when the water is high. I have such a recurring condition in one bathroom. I assume that waste from the toilet gets caught up on the junction of the shower pipe and the main line, and even gets pushed in with repeated flushes, eventually causing a slow draining condition, plunging is not a pleasant experience as that causes that stuff to be drawn up into the shower basin, but it happens infrequent enough that it’s not all that bad.
As such I doubt that routing the toilet will help, but routing the shower drain might.
plungers only work when the system affected is sealed and small. plunging a tub connected to a sink and toilet, with the plug after the toilet, will loose its function.
That tells me that the problem is not within the toilet itself, but somewhere in the pipes shared by the toilet, shower and washer.
Detaching the toilet from the floor may ultimately be the easiest way to get to the clog but don’t be misled into thinking that is an easy task. I am a landlord and I’ve done a few of these and there always seems to be some nightmare problem. Sometimes the bolts that hold it to the floor are rusted and you have to saw them off. Sometimes the caulk around the toilet sticks to and pulls up the tile. You’ll need to disconnect the supply line, and if you’re lucky the cut off valve will work as it should, but maybe not. Then there’s the wax ring. They are a mess. And there’s always dropping and shattering the toilet. I’ve done that too. Finally you’ve got to put it back in place.
Still that gives you the straightest rout to the pipes, so it may be worth the trouble.
My grandfather was a plumber. I love all plumbers. That said, I’ll just add one more factor into the bowl.
People don’t get PhDs & then become plumbers. I had problems with the line out to my septic tank. I eventually dug it all up & found the plumber my mom had hired years ago (& later told me about), rather than professionally attach an outdoor access port, had simply knocked a hole into the clay pipe with a hammer & stuck a piece of plastic tubing down into that! It had (of course) eventually slipped down, blocking the line. It was much less professional than anything I have ever done to this house myself. I solved the matter by removing the port, poorly patching the hole, and making sure no plant roots get into that. OK for 20 years now.
But, as said, it sure was disgusting. It is rather satisfying to pull clogs of hair out of your lines. Then again, if it’s blond hair, & you realize you don’t have blond hair. ARG!