Generally, I think you're on the right track to try to enforce some mechanical consequence to the choice of lifestyle.
I think the right choice is to use the second option more often than not. In specific circumstances (especially in social interactions), certain kinds of lifestyles should grant advantage or institute disadvantage. For instance, if you're a stable sleeper, and have to go in front of the Lord of the Town, you're likely to have disadvantage on all your checks. But the inverse is also true, if you're a hotel dormer, and don't make allowances, you're going to have disadvantage with the slumlords etc.
Again, I would make sure there are opportunities for him to...essentially pay...to remove some of this. For instance, if he's been slumming it for a few weeks, he could go to a bath house, pay a GP or two to get a good bath and get cleaned up. I might still harm him if rumors are floating about, but at least he'd look like he was supposed to be there. In other words, it shouldn't be a mechanical penalty that is permanent or robs the player of his agency. Just one that he has to work around occasionally.
As far as awarding inspiration, this should be very much tied to the BIFT (Bonds Ideals Flaws Traits) of each character rather than anything specific to their lifestyle. However, if they are (for good reason) entering a lifestyle that is in character, but conveys some kind of situation disadvantage (for instance, a Hermit staying in the woods, even if it means he misses something important in town).
Basically, inspiration is a reward for taking consequences for staying in character. So if your PC, within their character, decides to slum it, but then has disadvantage with the town noble the next day. That's actually cause to award inspiration, rather than the converse (rewarding them with inspiration for living an out of character lifestyle).
I would recommend doing the following changes.
- Expect the characters to reach level 12.
- Give the characters very powerful magic items.
- Reduce the CR 17 big bad to a CR 15 big bad. If the big bad needs to be level 17 to have access to a spell, ability, or collection of spells, then give the big bad an item which replicates that spell. (For example, perhaps the power comes from the building they occupy, combined with some artefact, rather than their own skill) Alternatively, you can reduce the CR by giving damage vulnerability, or fewer HP.
This should allow them to level up over 2 or 3 sessions, and give enough fights between levels to feel the achievement. The extra magic items will allow the big bad to be a challenge but beatable and you won't have to adjust your planned content too much.
My advice is partially based on the fact that the published adventure themselves don't actually take characters to level 20.
Best Answer
The Setup
I run a game using milestone XP, but rather than coming up with plot points, I planned out how many sessions we'll go between each level. This is because I felt like I was being internally inconsistent with when players leveled up, but I hate tracking XP.
I came to these numbers by looking at the general trends of how much XP it takes to get between various levels by default, and by adjusting based on how long I wanted to spend running this campaign. The XP chart doesn't follow a smooth function, but instead takes some weird dips, which I assumed were on purpose, and tried to incorporate into my chart. This means that I have a leveling chart, just not with tracking XP.
The Table
This is the table I've been using, but obviously, this is just what works for me. It might not fit other people's games, and that's fine. It's mostly here as an example
From level 1, there are 2 sessions to the next level.
From level 2, there are 2 sessions to the next level.
From level 3, there are 3 sessions to the next level.
From level 4, there are 4 sessions to the next level.
From level 5, there are 4 sessions to the next level.
From level 6, there are 6 sessions to the next level.
From level 7, there are 6 sessions to the next level.
From level 8, there are 7 sessions to the next level.
From level 9, there are 7 sessions to the next level.
From level 10, there are 6 sessions to the next level.
From level 11, there are 8 sessions to the next level.
From level 12, there are 6 sessions to the next level.
From level 13, there are 6 sessions to the next level.
From level 14, there are 7 sessions to the next level.
From level 15, there are 7 sessions to the next level.
From level 16, there are 7 sessions to the next level.
From level 17, there are 8 sessions to the next level.
From level 18, there are 8 sessions to the next level.
From level 19, there are 6 sessions to the next level.
The Solution
Using this, I would look at how many levels the XP from the item, be it the Deck of Many Things or something else, would grant in an XP leveling system.
To continue with your example, the Fool takes 1/3 of a level from a level 15 character. In my table, going from level 15 to level 16 takes 7 sessions, so I would make a note that that unlucky person will need 2 extra sessions to reach level 16. Or, if they draw the Jester, they'll level up 2 sessions early.
I keep track of this next to my notes on each session, which are separated and dated for each game; this makes it easy for me to keep track of when people should be leveling up.
The reason I go into all this detail is that I'm not sure, without some sort of standardized alternative to the XP charts, how to implement this, other than sort of winging it, which would feel unsatisfactory to me both as a DM and as a player.