Potential Levelling Changes

I've been considering for a while changing the system we use to gain levels, since XP presents a few problems with the way we run games. I'll outline the problem below, and then suggest a few possible solutions. Once you've read through the ideas, please vote in the poll so that I can get a sense of how people are feeling about this.

What XP is good at
XP is great at rewarding you for overcoming obstacles in game. Traditionally, XP is awarded based on the difficulty of monsters/challenges faced and thus what you do in a session directly impacts the amount of XP you get. This drive is great for motivating engagement and direct action in the session.

What isn't working?
If I gave out XP based purely on the challenges overcome in a specific session levelling could take between 5-10 sessions - since our sessions tend to be shorter (at least in terms of encounters) than a face to face session. Generally I like to level players every 3-5 sessions, since this allows you to get used to your new abilities and skills, but not get bored (You are never too far from a level up!) However, XP was not designed to work this way. I have been dividing XP per Level by the number of sessions I want you to spend at a given level, and awarding that for every session. This is using the system in a way in wasn't designed for, and leads to lower level players skipping levels (as happened to Kjartan).

There is also a strange thing in D&D where the difference between level 11 and 12 is actually less XP than the difference between 10 and 11 (there are reasons, however stupid they are...) which would mean, in our current system, a drop in XP for players of a higher level, taking on harder challenges...

A possible solution
I think the solution is session points:
- Every session you play, you gain a session point. This basically just accepts the fact that in our game, levelling is based on the amount you play, not the challenges you face in game (which is already the case).
-Each level takes a certain amount of session points, with most levels taking 4 sessions.
-When you are dramatically under-levelled (ie. <3/4 average party level), you gain bonus points (to help lower level characters catch up)

I think given the fact that we aren't using XP for it's intended purpose, we might as well make a system which is designed to do what we use it for! I am also considering options for a reward (other than monetary) for overcoming challenges in a session, if you have any suggestions please feel free to let me know.

I've put a poll below, if people don't agree with me that this is the best way forward, then we can leave things as they are. Any questions, feel free to post!

I feel like session points is probably the way to go given the level discrepancies we're starting to have

If session points seems right then lego. Personally I prefer xp based on achievements as its more satisfying. However I understand how session makes more sense for greater/larger players.

I prefer that too man, but that's not what we have right now anyway. I'm considering something that would supplement this system with this in mind, though not sure what yet.