It sounds like you had a positive result from changing the interval length of the healing tests.
One possibility would be to make the interval length dependent on the level of damage that the character is attempting to heal. For example, make the interval equal to (in days) the number of Physical damage boxes the character has.
If you're trying to heal 1P flesh wound, then the interval is one day. It's not bad, so you're fine the next day.
If you're trying to heal a 7P from accidentally falling on some bullets, then your interval is 7 days. If you heal 3 boxes and have 4 left, then your next interval is 4 days.
Compared to your current system, this would let minor wounds heal faster and major wounds (8P+) heal more slowly. A significant wound could lay a character low for a couple weeks, which might be a nice middle ground between a couple days (too short) and a couple months (more realistic, but perhaps too long for what's meant to be a game).
Just some thoughts.