As for resting, I was going to use a combination of a time pressure constraint and enemy reinforcements to combat long rests.
This is certainly a possibility, but one of the things I missed about AD&D was the long stretches of recovery time. This gives the dungeon denizens time to prepare new traps and ambushes. Is the party tearing through encounters with tactic A? Well, the goblins have had 10 days to come up with counter-tactic B.
Is the 1 or 2 Hit Die they could roll on a short rest really enough in your opinion to make the module to easy as written?
Slow Natural Recovery didn't have as big of an impact as I was expecting. It's definitely a lot funner than the default rules, but you can still expect the party to be at full or nearly-full health after a long rest. Yes, the party will be resting a little more frequently, but it's not like AD&D where they had to hole up for several days at a time.
That said, there's no perfect way to remove Hit Dice from the game without introducing new problems. For example, the fighter (with Second Wind) will laugh at your attempts to reduce his healing capabilities. Sure, you can make Second Wind a once-a-day ability, but I have a strong aversion to house-rules. Slow Natural Recovery has the benefit of being an official variant, and it doesn't introduce new problems, so I like it.
So, you (the DM) roll on all the Perception checks?
Yes. Here's an example:
The party has a Ranger with 14 passive Perception. They are walking toward a pit trap. The adventure text says: "It takes a successful DC 15 Wisdom (Perception) check to detect the trapdoor's presence."
You, the DM, roll a 1d20. Take the original DC, subtract 9 from it (15 - 9 = 6), and add the result to the d20 roll (1d20 + 6). This is the trapdoor's new DC.
Example: You roll 1d20 + 6 and get (4 + 6 =) 10.
Since the result is equal to or lower than the Ranger's passive Perception score of 14, the Ranger detects the trapdoor.
If you had rolled 1d20 + 6 and gotten (13 + 6 =) 19, then the Ranger would not have detected it.
This method has its basis in AD&D. For example, in 1st Edition, an elf had a 2 in 6 chance to automatically detect a secret door. So if the party came near a secret door, the DM would secretly roll a 1d6, and on a 1 or 2, the elf would detect it.