okay guys....an update - I think I am narrowing this down. Went through a few options again this morning - some repeated from before.
1)when I said it no longer worked on high speed that was because I had a loose line wire connection - likely because I did not retighten after one of my wiring dx changes. Discovered that this morning as I checked all the wires and now high speed works fine. So that info was misleading and confusing.
2) I tried low speed on all three of the control box circuits and all give me a moderate humming sound. Then I tried the high speed wire on all three of the control box circuits and have high speed working on each of the three buttons - so assuming the timer/control box is okay.
BUT now discovered this: While I cannot start low speed no matter which of the three timer circuits I use IF I have the pump running on high speed and then toggle to low (i.e., hit the low button after starting on high and while it is running on high) the pump will toggle to low and runs normally. I can toggle between high and low - back and forth - and get each speed - high on high button and low on low button. BTW the way the timer has always worked is that if it is running on one speed and you hit the other speed it just switches to that speed.
So, my lay person and technically uninformed assumption is that there is either too much resistance somewhere in the pump so that it can't get started on 'low', but once kick-started on high, low can manage to kick in. Or there is something within the pump (?) that is not functioning correctly. I am thinking it is within the pump because when I wire the pump directly - outside of the timer system - I still get the humming sound when trying low speed and it does not start.
Anyway if the motor is bad on low and would require expensive repairs or a replacement, I am content to set the timer to just run it on high.
AS always, thanks for all of your help.