Which optional rule or rules were you thinking about from the DMG?
Healer's kit dependency - pg 266
-This won't change anything besides someone having to carry and keep track of the kit uses, the in game cost is for the most part next to nothing. To me it seems to add just another extra layer of book keeping.
Slow natural healing - pg 267
-It slows down the pace of the game so if that is what you want sure. The end result will be more retreating back to town or camp. This becomes more of a grind than it is worth IMO, the party gets hurt to rest until they are 100% all you are doing is adding in extra fictional days to that rest time.
Rest Variant, gritty realism - pg 267
-This one changes up a lot of things in the game, most notable the power level of classes that depend on short and extended rests to recover abilities. Expect to see rogues dominating the game for example, they have few to no power that are rest dependent, and are great at conflict avoidance so get hurt less.
I think the best solution is to rethink how you look at hit points. They are not meat points. Every hit isn't a deep gash or fractured bone. Characters operate at 100% effectiveness at full health to that last hit point. It is that last hit point that matters.
A character can jump off a dragon, get breathed on, plummet to the earth and land in a spiked pit all in the same round, if he has even 1 hit point left he can keep going. So all I am saying is the luck, skill, divine intervention, plot armor that hit points do represent can come back amazingly fast because it is not wounds healing overnight, it is not bones mending, or twisted ankles correcting themselves. It is the return of plot armor.