If everyone wants to change the TL, I don't mind. But remember that the 'mood' that was desired by setting that lower TL was one of more gritty and realistic sci-fi. The things that are causing problems are not really part of that mood. AI has no place in Firefly, for instance, and was not a thing in the original idea.
Adjusting the TL up does not deal with the wonkiness of the tables. If we set it at TL11 --as an example-- we run into the problem that we can get Cybernetics that increase DEX +1, but not Gun Combat +1. A DEX boost is better than a Gun boost, as it does other things as well as adding to Gun Combat in almost every way (except for maybe 'analysing bullet patterns (Gun Combat plus INT or EDU)' or 'impressing someone with gun knowledge (Gun Combat plus SOC)').
It is less that our TL is too low, and more that their TLs make little sense. We (at least I) have only needed to look at the TL tables for these two things, so I am pretty sure there will be other places where it makes just as little sense. We will have to adjust things no matter the setting TL.
In those tables, the prices also don't make a lot of sense, but money in RPGs is always an issue --realistic money systems are boring-- and there is never really a problem making enough money to afford whatever we want, restricting availability is how you control access to stuff in RPGs. We were talking about Comms earlier, and they are ... Cr50! So, not a thing we need to worry about, it is going to cost you nearly KCr4 each month to maintain your ship and, like, KCr11 to fill the fuel tanks. You can by a cell-phone for each planet you land on without breaking a sweat.
More of a problem is that the prices, too, seem thumb-sucked. They are also inconsistent across the various books (not editions). I was looking at High Guard 2022 Update yesterday to work on the ship, and both High Guard and the Core book list the Free Trader, but at three different prices (MCr46.332, MCr45.792, MCr50.88), which are different to the price if we make it ourselves, or just add up the values on their table (MCr51.48).
All this says we should treat their tables as suggestion and guidelines.
I don't actually disagree with AI being at higher TLs by the book. Unless we want to have them be a common/normal thing we are still good with mostly TL9 and TL10. There will be areas where you can get stuff of level or two higher, but it will be 'prototypes' (maybe using the books rules for prototypes, but maybe ignoring them, or at least the hard-rule for weight). Most ships will be considered high-tech in most places, so we don't need to adjust the TLs of the base ships (which seem 'made up'). You can't get your ship repaired at the local farmer's mechanic, you will need to find a suitable ship-yard, possibly based on the Starport in the sector.
At the set TL, your having a ship with Jump capabilities makes you special. They are rare. Probably not rare enough that that is what Lio's navy wants from this one (you don't want to lose your Jump Drive to them), but rare enough that you can solve many problems just by having it.
If there is an AI on the ship, that could be a reason they want it. You will then have to decide what you do about that when you find out.
We also can have/find a sector/kingdom that is doing AI. This could be a cause for concern, or salvation... or both. The TL is not evenly distributed, so there could be places that are much higher in some fields, and higher TL stuff is around, just not stable.
Use the book as a guide for what is available, but ask if you want stuff that is listed higher, we can work out a plan.