From my own experience, if he's mowing 1/3 off once a week, it won't fill in any better with a shorter cut. Not to mention you would need to do the shorter cut just a couple of days after the 3.5 inch cut so you don't violate the 1/3 rule and scalp the grass.

 

I don't mean necessarily because it's shorter. I thought the mowing itself would stimulate growth, regardless of height of cut. If he mows to 3.5" on Saturday, I was thinking down to 2.5" on Mon/Tues and again on Thurs. I may have to actually do the front again on Saturday because it probably won't have grown to 3.5" by then.
2.5" is the highest my reel mower goes.

 

just mow it and maintain your own HOC for those areas and its not likely your service company blades will even cut a thing in said areas. No need to over think it. Just go for it and see what happens. Wouldn't even worry about the 1/3 rule for first cut. Not like we dont scalp our lawns for overseeding. It will recover perfectly fine in the fall.

 

Once a week mowing likely isn’t enough when doing the blitz. You’re right in your thinking. Mowing more often is a good step to help thicken the grass in general.