Before all considerations, you've got to ask yourself what is this particular optional rule trying to achieve.

In the text block preceding the one you quoted, you can find that goal:
>**Healing:**<hr> These optional rules make it easier or harder for adventurers to recover from injury, either increasing or reducing the amount of time your players can spend adventuring before rest is required. (DMG, p. 266)

By adding Healing Surges in combat, the DM aims to make hit points **easier to regain** between long rests.

Thus, allowing the expense of hit dice both in combats and short rests seems to concur to that goal.

As for the order in which things occur at the end of a short rest, it's up to the DM's decision (see it as *fine tuning* the difficuly of the game). Having the players use any hit dice left before regaining 1/4 of their maximum number will ensure they will have at least one to spend on the next encounter. On the other hand, allowing the 1/4 recovery before any short rest expense of hit dice will lead to healthier PCs at the start of the next fight.

**tl;dr : Yes, you can use both. On short rests, the DM decides if you regain some hit dice *before* you expend any, or the other way around.**