I seem to remember having a remarkably similar conversation, on a remarkably similar food run, myself.

Though I failed to articulate my ideas fully. As seems to be typical for me with oral communication.
For a Jack of All Trades Asset there are a few options.
As you've mentioned, one is to allow general skills to go up to d8, but cap specialisations at d10. Which is fairly fitting, given that the expanded name/phrase is, "Jack of all Trades, Master of none". And d12 level is considered "Master" in all the Cortex books I own.
Another option would be to halve (or otherwise lower) the AP cost of general skills and double (or otherwise increase) the AP cost of speciality skills.
Another option would be to combine the two. Halving the AP cost of general skills, but maxing out specialities at d10.
I'm reluctant to allow a single trait to allow all general skills to go to d8, or at least one named/themed "Jack of all Trades" as a d8 level is too high for someone who dabbles in many different skill sets.
Of course the other issue is, the suggestions so far (including mine) don't function strictly as Traits function. I may be mistaken, but as far as I know, all Traits are either wholly beneficial (Assets) or penalising (complications), they don't combine benefits and penalties.
The other concept I was trying to convey was a Role Asset.
Most RPGs, Serenity in particular, require characters to fill a particular role in the crew/party/team.
There are some Assets already which cover this. Born Behind the Wheel, Mechanical Empathy and Healers Touch to name a few. These all work by adding the Trait die to any rolls with a particular General Skill, or one of its specialities. There are several general skills which aren't covered by one of these assets. And maybe they don't need to be.
I can understand limiting what type of skills are effected by those kinds of traits, as things get very messy if they're involved in direct roll off situations. Namely, a pilot with BBtW who is flying against a pilot without it is surely going to win (assuming similar Attributes and Skills). However, most of the traits, the ones that boost Animals, Mechanic, Medicine and Tech aren't likely to be used in roll off situations. They're mostly going to be against target difficulties, in low/non combat situations.
Were there to be a "Combat Machine" Asset that functioned in the same manner, it would very quickly make any character with the trait overpowered (at least in combat situations) and then the GM is forced to have NPCs with the same Trait just to make things more challenging for the Combat character. Which quickly causes issues because the rest of the party who don't have the trait then find themselves quickly outmatched.
That said, I wanted a Trait that could be used to reflect a characters focus in a particular skill tree, while showing that they've neglected others to achieve that focus. Maybe that's redundant, given that where they spend their skill points should already reflect that. But in my opinion, it's too hard to get strong skill sets to represent that level of focus. And as I've mentioned, there aren't enough Traits to cover all the general skills, and some of them shouldn't be covered in that manner anyway.
So, back to the Trait.
The original idea I was working with, was something very similar to what etheral has presented (unsurprising since it was from the same conversation).
RoleChoose 1 general skill. You can now take that general skill up to d8, before having to buy specialities. However you must pick 2 other general skills which only go to d4 before you must specialise, and further, you must train 1 speciality within both of those skills to at least d6.
How much the trait should cost, I don't know. As I haven't done the maths to work out just how much of an AP advantage it is. But it could have several levels. The cheapest boosting 1 skill while penalising 2, the next boosting 2 while penalising 3 (or 4) and the last (should it have 3 levels) boosting 3 while penalising 4 (or 6).
But as I mentioned earlier, it functions differently to standard Traits, by combining an Asset with a Complication.