...Alright, imagine you and the boys were out hunting, suddenly Akatsuki, ringed and all ambush you with overwhelming power. You're now transported back to the hospital, and have been rewarded with the battle injuries debuff... Only this time it works a little different.
(Only once per death) Staying in a hospital bed for 1 minute (example), would lower the BI timer by a generous 30 seconds (example). Take note the debuff timer is vanilla, it will still be counting down like usual.
The engagement here is roleplaying resting in a bed like anyone injured really should.
A medic if present in the hospital will be able to perform treatment on a ninja reducing their BI timer by 30 seconds (example) the conditions are these;
The ninja who is being treated must be in a bed.
Treatment can be performed only once per ninja. If the ninja was already treated, another medic cant treat him to even more reduce the timer.
Treatment technique has a cooldown of 3 minutes (example) can be more to encourage there to be more medics working.
Treatment is a utility technique just like the Military Police Force has a jailing technique. I suggest creating a official medic organization for this, medics who wish to perform treatment would have to learn it by roleplaying with senior medics who then award them a certificate in the end which can be turned in for the technique. (Very relatable to the RP mission system, also gives it more depth like how you learned to treat people.)
Optional addition would be that the treatment technique is level-able which would make it so that the higher your level in it, the more seconds you'll be able to remove from the BI timer.
Here the engagement of course is actual medics helping ninjas in the hospital. You are hurt, resting in the bed, medic-san comes and helps you heal quicker by doing what she does best. (Presses a key to reduce your BI by 30 seconds)
Going inside the SPA in any village launches the "Relaxed" buff which every 10 seconds (example) removes 5 seconds (example) off your battle injuries.
A SPA must be added also to Takumi for this to be fair, but I'd give them like a sauna or something lol)
So you rested in the bed, had a medic treat you, now you're on your feet but not quite feeling OK yet, so you go to the SPA and chill out with the boys planning revenge on the Akatsuki while relaxing, healing your wounds in the nice warm water (or whatever the special thing there is xD)
Goal of this suggestion, breathe life into the battle injuries system, make it a thing where players engage with each other, just imagine how popular SPA's will become. It will make the mission harder, but it will be worth it. (Perhaps buff mission exp for visiting foreign SPA lateron)