For the purposes of this conversation, I will refer to the light-prep sandbox that is created as the game unfolds as a pseudo-sandbox...
I would prefer quasi-sandbox.

For the purposes of this conversation, I will refer to the light-prep sandbox that is created as the game unfolds as a pseudo-sandbox...
Right off the bat, I'm going to throw a proposal out here. Ditch the Experience Point system. It is cumbersome and, frankly, encourages a style of play (that is, combat-driven) that will make your life more difficult.
Some DMs simply advance PCs whenever it feels appropriate. If you would prefer a little more structure, however, I recommend advancing the PCs in level as they accomplish quests (say, 2 major quests, with 3 minor quests counting as a major). There is some degree of tweaking that you can do here, as well. For instance, if you want earlier levels to come quicker than later levels, you could add 1 major quest to the total needed every time a level is achieved.
With this simple substitution, we eliminate the need to figure out how much XP a party earns, how to divvy it up, how many combats you need to plan for so the party can level, and how to advance the PCs if they take an approach that isn't combat. These things may not seem significant, but they add up, and they eat away your prep—and playing—time.
- [WARNING: controversial topic] As as experiment, I would like to try a strange approach where I would use XP as a reward for players' efforts rather than achievement. Thus failing to defeat the BBEG in combat would still result in XP earned as long as the players didn't play poorly.
IMXP most players really want to receive XP points after every gaming session. But I agree that since they don't need to know how you calculate them, you don't have to calculate them by any rules, you can ad-lib your XP rewards based on how often you want them to level up.
- I want my players to be focused on advancing the campaign plot (if any) and completing adventures. I don't want them to go looking for random encounters to level up and be stronger for the next chapter, in fact I prefer random encounters to be a punishment for wasting time. If you're of the same opinion, you may want to let the players know that random encounters and unnecessary combats (from the story point of view) will give them reduced rewards, maybe 50% XP and treasure, or something like that.
That's fine IMO, as long as you don't allow 'farming' of the same unkilled foe.