I think the AI needs some help when playing as Minbari.
There's at least two issues that the AI seems to have problems with :- the tech tree and the cost of ships at the start.
These two factors means Minbari AIs tend to dig themselves in at their homeworld and rarely expand & colonize new worlds.
I've just played a large map where all 8-players were Minbari, and only one AI colonized several worlds (6, then 8).
Just two AIs built more than one cap ship, the AI that colonized managed to build 3.
It was very easy for me to expand (30+ planets) into unclaimed territory.
I can see the intent of the Minbari tech tree was to prevent the AI walking over EA, Narn & Centauri neighbours.
However, it seems that it may be a bit too difficult, if the AI makes the mistake of not building any civilian labs it cannot do any research on any of the other trees - civilian tech The Early Years is a prerequisite for everything.
As it very hard for a Minbari AI to colonize at the start, they have a big handicap in developing their economy.
This coupled with the expense of their ships, means they rarely build a decent fleet in the beginning.
I suggest a few tweaks to give the AI at little help.
1) Allow the Minbari to colonize desert worlds without Star Bourne research - like the previous version of SotYR IIRC
2) Make the Tinashi the Minbari's first capital ship, Sharlin would become available after research.
OK, I've suggested this before, but I think the high cost of a subsequent Sharlins deters the AI from building them, especially as the Minbari economy as quite hard to get going.
Starting with the Tinashi would balance the Minbari against EA/Narn etc, while at the same time may make it easier for Minbari AIs to build a decent starting fleet.
3) Maybe also spread the cost of capital ships across the different resources more evenly, less metal, more crystal.
Minbari have several techs that improve crystal extraction rates, plus their ships use polycrystalline armour.
4) Pure conjecture here from a non-modder, but does the AI treat each tree position with different priorities?
If so, it may worth be swapping the Worker Caste and Ruling Body trees so that higher priority is given the latter - as that tree has techs that are prerequisites for techs on the other trees.
It seemed that AIs didn't do much work on Ruling Body (aka Diplomacy tree) which hindered their research opportunities elsewhere.