The issue at heart is that default Colemak has this same slight imbalance. A key design consideration of Mod-DH / Colemak-CA(W) is to keep keys on the same fingers, so of course it inherits favouring the right-hand side.

I think it will be difficult to do anything about without having a lot of unintended knock-on effects.

As you found, with your L/P switch, it might be not very good for same-finger bigrams. As well as MP and LT, I also worry about PH.

It reminds me though, I also once played around with the idea of a layout that would move L to the left-hand-side:

Q W L P G J F U Y ;
A S R T D H N E I O
 Z X C V B K M , . /

It's based on default Colemak, the idea is to return S to its Qwerty location, and have R and L on the same column, since RL/LR are fairly uncommon bigrams.
The bottom row returns to default Qwerty too, but you'd type C with index finger to avoid the CR and CL bigrams (so called "alternative" fingering in my analyzer).
Obviously it doesn't fix the DH centre column issue, but you could introduce a D>P>G and H>M>K rotations to fix that.

It gives you a hand-balance closer to 50:50, but at a cost of slightly worse same-finger ratio and more keys switching sides, and D and B positions are not so nice.

So all in all, you're probably better off leaving things as they are.

Yes, that's the end I arrive at each time I try to modify something on the layout. It would take more than just moving a few keys around on the upper row to achive a hand distribution close to 50:50.

I would already be content with 0.49:0.51. I just really want to bring that 0.45 higher.

Yup, it's indeed odd. I used the ergonomic configuration and it shifts X by one key to the left. However, it doesn't matter which configuration you use, finger frequency is going stay the same, which I ultimately would like to fix.

That's true. Altough I do type X with my pinky on ANSI as it feels more comfortable. For me to be able to hit it with my ring finger, I have to curl my finger in an awkward way which feels unnatural. I also have to slightly raise my pinky off of the keyboard to be able to achive this.

Perhaps it could also be beceause of the fact that I used to type on ISO keyboards, but I moved to Poland where ANSI dominates on the market.

No, I didn't count the space bar. Although I believe, you're right as pressing space with the left thumb could ease the feeling of ‘over working’ my right hand (as well as change the hands percentage distribution on paper) as I do press the space bar with my right thumb by reflex.

I guess I'll have to work on getting my left thumb used to ‘spacing’.

Ah, okay, that makes sense. Yeah, I've been manually modifying the configuration for the tests I'm running today.