I'm of the opinion that Jaina's J should be her signature card, it feels strange to me that an archer's arrow card would be among her worst options to reveal.
From a fluff perspective (and from the FSFG) I really like the thought of her slow J having knockdown. This would provide a great dodge follow up and allow her to set up crossups and straights, which she excels at, without spending any throws/blocks to do so. I could also see it being more damaging than Graves J, say 10(9) damage to keep it to an increment of 2 damage. This would allow her to make much more efficient use of her dodges in the early game when she is block starved and also whenever she is outsped by 2.2/2.3 speed in neutral or by 0.0 speed DPs.
This change also makes slow J a truly formidable throw punish, even without follow up, which Jaina sometimes is stuck without in the early game. It would particularly help her versus Zane, one of her worst matchups, who hates being knocked down, and it would trade very nicely with his K.
In terms of addressing her card flow, how about if fast J had a J* ability which gives her something like the higher risk version of Graves J:
Feeding the Flames: When you deal block damage with Flame Arrow draw a card
This way she can use the fast side to build her hand along with her opponent, escalating the game. If she then uses her innate, the net bock damage is only 2HP so its either gain cards for 2 net damage or cycle cards for 5 block damage.
In terms of a fast J speed boost, I reckon 2.4 speed is essentially a non-issue for balance since she has unlimited 2.4 speed K once she draws it. Unlimited 2.2 speed would probably reduce her zoning game play in most matchups, so I'm less keen on that as a first pass solution.