Yes that's the route i intended. Bit of a roller coaster. Looks fairly flat after the String Rd. Sounds like Machrie golf course will be a perfectly timed cake stop.
The Ross Rd climb comes in at no 5 in terms of average gradient in the pocket book "Cyclists guide to Hillclimbs on Scottish Lowland Roads" , The String from Brodick is no. 10. It doesn't include every climb out there just a selection.
No. 1 is the climb up East Lomond near Falkland "Purin Den" avg grad 10%. I got that one out the way a couple of weeks back (in fact the day of the Kinross sportive). Pretty tough going! Fantastic view from the car park at the top.
Machrie does look like a good spot to take on food, with a flat section just after it before the final climb beyond Lochranza

, then it's flat-ish/rolling terrain into Brodick.
Sounds like an interesting wee book of climbs you're working your way through
The
Purrin Den is on Strava as what looks like a club hill climb route too - 2.2km at 10.2% ave - nice! (Same road that Tug found).