Yeah, so I did mine in mid finger DIP joint. The specialist got me to wear a moulded plastic blocking splint 24/7 for 6 weeks to avoid any possibility that the finger could hyperextend (or even go to totally straight) at that joint - essentially holding it in flexion. After that 6 weeks there was a reduced range of motion due to the scar tissue, but he said that that was basically the point - the splinting gave it time to rebuild. (There was also unwanted reduced range of motion in the PIP joint due to the splint). I gradually wore the splint less and gradually increased range of motion by simply trying to move the finger through the whole range voluntarily when the splint wasn't on, and then later by stretching only at the (uninjured) PIP. I didn't stretch the injured DIP joint and he didn't recommend that I did so, though I never asked.
If the injury is healed and scar tissue is the problem then stretching to increase range of motion might work. If, as it sounds like you think is the case, there's still an injury then stretching it into extension would presumably just reinjure the volar plate so tread carefully unless you're sure the original issue is fixed - stretching the injured PIP into extension to fix it sounds analogous to hanging off crimps to fix a pulley injury: sure you have to do it again gently and gradually once the initial fix is done, but if it's at the acute stage of the injury then it sounds to me like a bad idea.
For reference, mine never really hurt or swelled, it just felt 'funny'/weak/exposed and the injured joint naturally sat in a hyperextended position by a few degrees (you could even see that on the x-ray). I could climb on it but shouldn't have been doing so - was doing hard boulders open handed (DIP volar plate means crimping is the enemy) until the day before I saw the specialist and he unexpectedly told me it should be in a splint!