I beat your restart by a week. (See, the competitive urge never goes away!)
I got my circa:1999 restart going by riding with my daughters down to the bookstore on weekends, 5 miles away, where we'd sip fancy coffee and browse the books. My wife would take anyone who was too tired home, and I'd ride back. Fast forward a few years, and I started commuting by bike: same kind of thing, only separated by 9 hours instead of half an hour, and every day. That really build up my endurance over a few years.
So yes, I think resting for a few minutes and repeating the lap is going to be good. Probably not as good as doing the whole thing straight. Best I could tell, I got an endurance benefit of about half the shorter ride when doing two rides a day. (Liberal Kentucky windage applied!)