The rubbery texture can be from over-kneading when combining the burgers. For some recipes, I have pre-baked at a low temperature then grilled to get the right texture on the outside. This would work with a recipe with a resting period as well as one that just dries.
Also, if the egg replacer is not binding correctly (I am assuming you are using Ener-G), try using a chia or flax egg (1 tbsp of either milled, then combined with 3 tbsp water and set to congeal). This will raise the moisture in your patty, which likely already has a good amount based on your recipe, so you can use other wet ingredients instead of adding water.
These are two related, but different products.
Gluten is protein that is formed from two pre-cursor proteins, glutanin and gliaden, found in wheat flour in the presence of water and under enzymatic activity.
It forms resilient stretchable networks which give yeast raised bread its structure.
Whole wheat flour is... well... whole wheat berries, ground up. It is mostly starch, but contains all glutenin, gliaden, and the necessary enzyme to create gluten, which forms naturally when the flour is moistened, if given long enough or kneaded to accelerate the process. However, even a very "strong" flour (bread flour) will have no more than about 10%-15% percent protein by weight, so it cannot form more than that amount of gluten.
Vital wheat gluten is essentially concentrated, powdered gluten, without the rest of the parts of the wheat berry.
They are not freely interchangeable, as the gluten does not bring the starch, bran, and other components that flour does. You may, in specific recipes, be able to use just gluten, but not in the general case. And even if substitution is possible, you would have to determine the correct ratio to achieve the desired outcome.
Using vital wheat gluten in lieu of whole wheat flour, in most applications, will either fail completely (no thickening from starch, as in a gravy), or be dense and rubbery, and practically unpalatable (as in a bread).
Best Answer
One way to avoid the vital wheat gluten taste is to develop wheat gluten directly from flour (a somewhat popular food in China). To do so, make a dough of bread flour and water, knead it well, rest 2-3 hours, then "wash" the dough in water until most of the starch has been rinsed away. The result is a high protein/water mass that I assume could be used in faux meats, that will taste highly umami (from wheat protein's glutamate), but not unpleasant like vital wheat gluten.
To wash the dough, submerge it in a bowl of water in the sink and rub it (like handwashing clothing). Change out the water until it turns clean. This process can take ~15-30 minutes and 10+ changes. It's a hassle, but the result, if done well, will have an amazing chew and flavor.
This method has a low yield. One method to increase it involves adding a small percentage of vital wheat gluten to the flour. This increases yield without really effecting flavor, though adding too much can make the dough unpleasantly tougher. Another method to increase yield may be to add salt.