Your problems stem from the way the flour is NOT being properly coated by the drippings, because they're too much of a mix of wet and fat. It's an easy enough problem to solve. However, you specifically asked about a gravy made without drippings, so I'll tackle that first.
Option A: (1) Make a turkey stock from roast wings and necks bought for the purpose, and/or from a turkery carcass from a previous dinner, you may add some wine to the stock if you desire; (1a) If you don't have time to make a turkey stock, just use boxed or "better than bullion" stock. (2) Prepare a roux made from equal parts butter and flour; cook at least until the "raw" is off the flour, and perhaps a bit farther. (3) Pour a little hot or room temperature stock into the hot roux, and whisk until the mixture thickens. Continue adding stock a little at a time and whisking until thickened until you have the desried amount and desired consistency. (Note that a typical gravy consistency is 2 tbs butter, 2 tbs flour to 3 - 4 cups stock.) 4. Sieve the gravy.
Option B: Make a chicken or turkey veloute, in the normal way. Add to it as you will.
Option C: Do as Chef How described, only making the roux with butter, and adding it to hot stock instead of the other way around; or you may use beurre manie instead of roux, and sieve. Seiving will not take the raw taste away from beurre manie but it will improve the texture.
If you are adding mushrooms, giblets or anything else to the gravy; try and fit a sieving in there before the additions. If you can't, you can't, and don't worry about it. Since you're not using drippings, and are perhaps using chicken stock, you're gravy will have drifted from away from the intensely turkey. That makes the additions even more welcome.
Really the same as without, but with one technical difference. The trick to avoiding all of the problems you mentioned is separating the fat from the drippings, and adding each in its own time. That is: Pour off the liquids from the pan, allow them to settle, and separate the fat from the juices. Use a controlled amount of relatively pure fat to make the roux. Use the stock or wine to deglaze the fond, and add the fond and defatted juices to the roux, as a preliminary step to adding the stock (again, in stages).
This method, along with chopped giblets, shallots and mushrooms, is how I usually make mine. I find dry Vermouth wokds very well as the wine, but of course the choice is yours.
Your pal in turkitude,