Sometimes it just makes sense to move on a gobbler you are working. This is particularly true of "hung-up" birds that for one reason or another won't come in. However, moving is a risky maneuver because if that bird spots you, your chances are zip.
If you decide you must move, make your plan in advance. Know exactly where you are going and how you are going to get there. Next, make sure you know where the gobbler is and that he can't see you. Often gobblers will walk back and forth as they gobble and strut. Time your move to when he is farthest away. Moving on a silent gobbler is a bad idea, since he may be on his way. Make your move without hesitation. You've decided on this play, now execute it.
Don't leave your decoy standing behind. More than one hunter has successfully moved, only to have the gobbler change his mind and go to the decoy left at the first set-up spot.

Henned-up gobblers are one of the toughest challenges in turkey hunting. Hung-up gobblers are a close second. A gobbler with hens may answer your calling but will seldom leave them. Many times the hens will try to lead the gobbler away. When a gobbler answers but moves away, it indicates he is with hens.

A stationary gobbling bird that simply won't budge is truly hung up. Often he is across a creek or some other obstacle he doesn't want to cross. Sometimes he is in his favorite strutting area and doesn't want to leave. Frequently the hunter unknowingly encourages the gobbler to stay put by calling too much, convincing the gobbler the "hen" is on the way.

One strategy for versatile hunters is to change calls or style of calling. Another is to simply shut up and play hard to get right back. The third, and most risky, is to try to change calling positions to shake the hung-up gobbler loose.

The use of calls imitating the gobble of an adult male is somewhat controversial. It is an excellent locator call. It also can attract a dominant gobbler looking for an intruder in his territory. However, gobbling has some tactical downsides and involves safety considerations.
As with bugling to elk, gobbling at a gobbler with his harem hens may make him decide to leave and take his girlfriends elsewhere, away from competition. If you sound too big and bad, it also can cause sub-dominant gobblers to shut up and leave the area.
Of course a well executed gobble will attract other hunters. Having other hunters sneaking in, literally hunting you, is potentially dangerous and is almost certain to at least mess up your hunting area for the morning.
Restrict your gobbling on public or hard-hunted land as a matter of both common sense and safety. As a turkey hunting tactic, it's a judgment call as to whether it will draw in a particular gobbler or drive him away.

The proper use of blinds and decoys will certainly help any turkey hunter. It's hard to be too well camouflaged or to have too much "attraction" working for you when hunting wary old gobblers.
A good blind hides you but doesn't hinder you. Natural brush blinds are O.K. but they limit your ability to move if necessary, and they take time to build, which creates some disturbance in the area. The best turkey blinds are those with camouflage netting and a few stakes. These are lightweight, very portable and quick and quiet to set up and take down.
A turkey decoy will surely attract a gobbler, including those that can see the decoy but may be out of calling range. However, for a bowhunter, they give the gobbler something to focus on while the bow is being drawn. They do a similar good job for the gun hunter who gets caught with his gun down.