just out of curiousity- If the gluten in a starter is extremely degraded to the point of "glueyness" will the small amount of starter used affect the quality of the final dough?
If the starter has aged to the point you describe, I'd give it two or three feedings before using it in baking. Once it is back to a healthy condition, you'll be able to make bread with the characteristics you desire.
Having had a starter that was consistently unbalanced (i.e., high acid production and very aggressive gluten attack), I can tell you that the resulting bread wasn't all that good. The dough broke down faster than it inflated, was very sticky even at lower hydration levels, and never behaved well. Once I got the starter nursed back to health, the bread improved, too.
If you just fed your starter, and it's still "gluey" I'd think you have some other problems going on.