...but since his patron is likely the pre-eminent source of his tithed income, one can imagine it would be important to him. I think of Brandon's description of the Delaford living to Elinor in S&S as "capable of improvement." I wonder what that means, since Mr. Collins (and Charlotte) would naturally be interested in improving the living if possible.

First, I imagine, one would have to stay on the right side of the members of the parish one has (especially one's wealthiest members). Beyond that, does "improving the living" mean attracting more locals into the parish (via Mr. Collins's naturally witty and gratifying sermons? LOL), or is it by upgrading eh house and lands to provide more income (since IIRC at least some rectors controlled farming plots which they might be able to make more efficient)?