I proposed something in another thread, don't remember which one, but I'll repeat it here.
Tie DITR's to the draft. Only allow DITR's to be bestowed upon draftees . . . tryout camp guys and IFA's are ineligible to become DITR's.
You get one DITR for every 4 draftees you sign beyond the 5th round. Sign all twenty 6th through 25th rounders, you get 5 DITR's. If you only sign your 6th through 10th round picks, you only get 1 DITR. Don't sign anybody beyond the 5th round, you get nada.
An additional restriction: only draftees who are still with the franchise that drafted them, and who have been promoted to a level appropriate to their experience, are eligible for DITR.
This suggestion encourages both (a) signing your draftees, and (b) promoting them (to reduce risk of retirement). DITR is your reward for doing what you should be doing.