Running and gunning is fun but I kill a lot more turkeys staying put for longer even taking a few naps, I have been woke up by gobblers that came in while i was taking a nap. Sure I might miss one of two doing that but those naps are some of the best sleep i ever get.
Decoys, DSD are the most realistic that i have seen, good quality as well and if taken care of will last for years.
i carry my decoys in the pouch on the back of the turkey vest, it is big enough for my deeks and a turkey.
running and gunning is a lot of fun and can be effective but as I have gotten older and less mobile i do it much less.
Scouting is a big part of success and if you are where the turkeys want to be or between them and a desired location they are much easier to call in. Do not discount the middle of the day, I have killed a lot of gobblers from about 10 to 3 in the afternoon, once a gobbler breeds the hens he gets around him in the morning he often can be pulled away form them with a bit of calling.
A Tom I killed last year and one the year before both came down with hens near my setup and wandered off with them ignoring my decoys and my calling. Both birds I ended up killing late morning after they came back alone. Knowing this is common, at least on my lease over the last 20 years, I take an ear bud to listen to the radio on my phone and those wonderful naps to help stay with it as long as possible. It is real tempting to get up and move with them or to distant gobbling birds, but as long as I know that initial bird saw my decoys and heard me, I stay put.