John, I cannot thank you enough for the time you're sharing!
I do intend on having 'pros' do the actual work. I spent too long learning my trade to not have respect for my fellow tradesmen!
Perhaps you misunderstood my description. I'll try to get a sketch scanned, but until then I'll try words (again).
Overseas I saw commercial kitchens that were plumbed so that the sinks had simple, straight pipes dropping straight down from the drain, to where they ended (maybe) 3" above the floor. Set in the floor was a trough with a grating over it; this trough often served several sinks, and typically came out from under the sink only at the end. At this end there was a much-enlarged cylinder dropping straight down, where it conected to the drain piping at the bottom. Into this cylinder sat an easily-removed basket for catching large materials (like vegetable peelings)
In short, with this arrangement you would not have the 'toothpaste flowing across the floor tiles.' You would give any overflow, or splashings, from the shower area, another place to drain. This would be in addition to a drain placed within the shower area proper. I had forgotten about these 'floor sinks' until I read your other remarks about wanting there to be a secondary drain.
For the moment, let me try to explain the proposed layout:
Bathroom is about 8ft. x 10ft. As you stand in the doorway, you are looking across the 8ft. dimension. The wall on the left is about 2ft. to the left of the doorway, and the wall on the right is more than 5ft. to the right of the doorway.
On the left wall is a bathroom sink, a hair wash sink, and the toilet. On the right, as you enter, is a shallow linen closet and a glass shower partition, perhaps 40" long. After the partition is aa 'aisle' between the shower area and the tub. The tub is set with the short end opposite the toilet, and the long side along the far wall. This arrangement gives you a shower area of about 40" x 4ft. "within" the partition, and 5ft x 4ft if you include the 'aisle' as part of the shower space.