Auto retriggering timer for between 1-15 seconds (1, 10 & 15) and between 200-1000 Cycles ( 200, 800 &1000)

I'd attach a ladder of resistors and an analog input to the rotary switch like:

per:

Then read analogRead() it, and do some integer arithmetic to get a 0-4 (maybe mode = (analogRead(modePin)+102)/226 ? ) and use that to choose the mode.

For the different blink timers, I'd try an array of struct like one of these LED blinker solutions:

but and add in an extra variable for "count".

Your box looks like it has a couple buttons for start &stop an you could use one of those to reset the count.

Since there are several analog inputs on an uno, you could handle all the knobs and buttons on that box and more if you like.