Michelle, I see your problem and I have chewed on it ever since.
I can only offer my suggestions which might not be wholly accurate but might unlock the knot for you a bit more.
If I was determined to weave this pattern on a jack loom I would have to approach it in one of two ways. Either weave the darn thing upside down by tying it up at the draft suggests, or re-engineer the treadling draft. By re-engineering the treadling I mean that I would start at the known points of what the draft is intending to achieve and work backwards from there.
Firstly - how many treadles do you have? (I am assuming 8.)
So the first thing the draft is saying is "no tabby" - that automatically gives you two free treadles.
The tie up is suggesting that you have covered warp threads on shafts 1,2,3 &4. But if you look at those shafts which are used individually in the treadling, only 3 of the four are used (that is 1,3&4) - this frees up another shaft if you want.
So the tie up for these three shafts on the jack loom you know how to do (fill the blanks!)
Then let us see what else the draft is saying to you. The tie-up is saying to use two treadles at once - to achieve, what? OK to cover warp threads in pairs. The draft is covering warps on shafts 3&4 , 2&3, 1&2, and 1&4. That's another 4 treadles needed if you tie up to achieve this. (the blanks for the jack loom). No need to depress two treadles simultaneously - which eliminates your dilemma.
Therefore you have used 7 treadles to achieve what the draft is asking of you.
Furthermore you could achieve a basket weave and a 2/2 twill for hems etc. with this tie-up
Not sure if I have made any sense, or indeed if this has just been an almighty Goof - but that is the way I would approach things - and I guess I would find out the 'error of my ways' whilst at the loom!!! 😃
Good luck!