I run into this problem on our club rides. On my own I don’t stop for much more than a nature break. The club, great fun folks that love to stop and eat. I just accept that I’m going to hurt on the start after the break. The worst is when the lunch stop comes at the base of a steep long climb…..Oh well, 1st world problems.
Those stops before a long hill. I stop "AFTER" a hill and ride over the top. If it has been a hard climb then I also slow down- get into a low gear and spin till the legs recover. By that time it is normally too late to stop so just carry on. I used to do the Salisbury 100 and it is a fantastic ride except at the 50 mile mark you had an enforced 30 minute timed stop. Lunch was provided and it was a good snack. Problem was that 5 minutes after was Brassknocker hill. It was steep and it was long but I think most of the effort involved was in getting cold legs to work by the time you got to the hill. That hill always seemed steep to me but probably wasn't.
But that is on the road. Offroad and round here there are plenty of tough steep hills. We have a rule in our group and after the long hills the group will reform. That means that the front runners will have a long break before the last rider gets there. When I used to be part of that front group it was hard to restart so I used to keep cycling slowly to the next gate. By which time they would have caught me and I was ready to open the gate for them.
Slowing down when tired works providing it is not for too long and has even worked when I bonked. Realised I had bonked- Downed a bottle of drink- took a couple of energy bars and rode slowly till I recovered. At least I was moving all the tim instead of stopping and never restarting.