Since this is a "medical" and as such might be a temporary need, and you say you have no desire to run more than one head at a time, the simplest and least invasive would be to replace your existing shower head with a hand held retrofit kit. Yes, you can buy additional brackets so the head can be mounted elsewhere on the wall. And you are correct, the bracket needs to be matched to the head, they are not necessarily universal. A lot of showers I build, I also make a teak bench for them. In addition to an extra bracket or two on the wall, often times I'll add a bracket to the edge of the bench. I'd look for the longest hose you can find. Personally I find the segmented metal hoses lay flatter and loop over themselves less than the plastic hoses. Plastic versus metal head? Plastic is fine in a decent head, but in a $9.00 head the entire thing might be too lightweight and spray water everywhere regardless of what material it is made from. Mongo

Thanks! The problem leak is from the spout while the water is off, which we initially thought was valve-related, but doesn't seem to be now that the new valve is in and it hasn't stopped. It's a slow but steady drip. We do also have problems with a steady but small stream of water from the spout while the shower is running (and with a small stream of water from the shower while it's not supposed to be running) but those stop when the water is off, so I'm less concerned about them.

Get out of the big box stores as you can certainly find diverters to create what you want in a real plumbing supply store. I have no idea why the strength of the shower arm is at issue since the shower heads are attached separately from the diverters. I am also not understanding why you would have a diverter OUTSIDE the shower since the purpose of a diverter is to enable a person to change the source of the water INSIDE the shower. I am not seeing any advantage in terms of maintenance or installation to having one diverter which is inaccessible while showering. My controls are completely accessible from outside the shower because they are near the entrance of the shower so I enter the shower when the temperature and source of water is what I want and then I can adjust while showering. However I think you still are not grasping that you need to buy everything from the same brand since the trim (shower heads and what you see) needs to match the rough (e.g. the actual diverters and other mechanisms). Pick the "trim" you like and tell your plumber or GC what you have selected and what configuration you want and then have him order exactly what is necessary. In terms of pricing, generally Delta and Moen are the best quality for the money. Delta is guaranteed for life and parts for repairs if necessary are always going to be available and will fit.

I'm in California and recently remodeled with a three way diverter and I am familiar with the restriction - e.g. that one can have only ONE water fixture on at the same time. However, I am confused by your question as my three way diverter turns each fixture both selects the fixture and turns it on. In other words, mine operates like a clock - e.g. it everything is over when the lever is at 6 PM - my overhead shower is on at 3 PM - the handheld by my bench is on at noon and the handheld shower head by the standard shower head is on at 9 PM. I have two adjustable shower heads and one fixed shower head because I wanted an adjustable by the bench. I also have a thermostatic shower so the trim which adjusts the temperature only is directly below the three way diverter which turns the water on/off and selects the fixture. Do you have a three way diverter because you have a tub/shower combination and so you select between shower and tub filler fixture? As I posted, I opted for one fixed and two adjustable shower heads in my walk in shower.