Crowded grape shoots

My two grapevines are vigorously shooting now, but most of the shoots are coming out from a couple of locations causing extreme crowding. I spaced the trunks and branches nicely before, but some sections have had no shoots for the last couple of years. Not sure if they’re dead branches.
The worst crowded area got severe mildew last year, and I lost most of the crop. Is there anything I can do other than just cut back all of the shoots except for one or two and have a very small crop this year?