He can ignore his wounds and "press on" five minutes after he receives them and he can ignore his wounds and press on a day later.
No problem.
And if he gets hit again 5 minutes later the effect of being wounded makes him less capable of continuing to press on. A later strike is more likely to take him out. With surges the next morning the character in either scenario is back to full capacity.
There is more than one element of being damaged and you are only attending to one of them. Your system still fails for the issues you have ignored. Yes, you can role play still being wounded, but the mechanical behavior of the system, treats this guy exactly the same as a fully healed guy because as far as the system claim he *IS* fully healed.
That is partly an issue with the base hit point system. Apart from the ability to avoid taking or succumbing to future wounds, a character with 1 hp remaining is no different from the same character when he is fully healed. As mentioned in the previous post, you can flavor this one of two ways: either he has taken no serious wounds, or he has taken serious wounds, but is otherwise able to act as if he had not.
The 5 minutes after being hit guy is just as good at striking and avoiding as an unwounded guy.
The striking bit is due to the base hit point system. Avoiding is only applicable if we define hit points as the ability to avoid serious injury (the first scenario), and if we do so, the character would not have sustained any serious injury in the first place.
Alternatively, it is possible to take a hybrid approach in which hit points can be defined as either the ability to avoid serious wounds or the ability to press on despite them. You can still get a consistent narrative, although once a character is narrated as having taken a number of serious wounds, it is probably more plausible to narrate subsequent "hits" as being minimized or avoided instead of sustained and ignored.
But but there are differences between this guy and a truly unwounded guy in other parts of the system.
Such as? Apart from the ability to avoid future wounds (the first scenario) or the ability to press on unhindered despite the sum total of the wounds already sustained (the second scenario), I am unable to recall any significant part of the system that treats a character at full hit points and one down to 1 hp any differently.
In either scenario the guy is just like unwounded guy the next morning. There are other systems which are superior for handling this situation and therefore the surge options is unacceptable.
Yes, after an extended rest, the character's vigor, luck or whatever it is that allows him to avoid taking a serious wound in the first place are restored (the first scenario) or his reserves of willpower and determination, or whatever allows him to ignore the wounds, have been refreshed (the second scenario).
As I mentioned in my earlier post, while it might not be an approach you are used to or are comfortable with, I don't think it's fair to say that it is dysfunctional, convoluted or unacceptable.