Players get pretty disappointed when they roll poorly for HP. And then they get annoying when they start asking for refills. So how about if we tie HP roles into the Lifestyle rules and turn what is otherwise a mildly annoying tax that is frequently ignored into a reward and something the player really cares about?
HP Re-Rolls Based on Lifestyle
Wretched: reroll Max, Max -1 and Max -2
Squalid: reroll Max and Max-1
Poor: reroll Max hp
Moderate: no reroll
Comfortable: reroll 1s
Wealthy: reroll 1s & 2s
Aristocratic: reroll 1, 2 and 3s
In the fiction this simulates the long term effect of Lifestyle: if you sleep comfortably and eat better you are more likely to have higher hp. Go cheap and live in a dockside flophouse, then you are more likely to be less robust. In the fiction there will be outliers like the frail noble or the hearty street thug, but that's a result of the CON modifier.
Example: a Wizard gains a new level and he's been cheap and living in Poor conditions. He rolls his new d6 HD and gets a 6. Too bad, due to the poor conditions he's been living in he can't take the roll.
So, what's the impact of living on the road? Personally I would tie that into rules for creting Camps, but that's another topic.
Also, I would be inclined to have characters re-roll hit points if their Lifestyle changed for a significant length of time (maybe 1 week, maybe 1 month). This is an aspect of the rule that players will most likely hate but I think it helps provide mechanical consequences for in-game behavior. Get locked in prison? You're health may take a hit until you get out and can spend some time living better. Get wined and dined by a Prince? You'd be surprised how good that feather bed makes you feel.