It could be done.
All based on assumed finishing positions, but lets say we finish 16th, West Coast finish bottom and Freo finish 13th (obviously people will have finishing positions different but this is a guide that we aren't far off what we want).
So our picks (I haven't allowed for priority picks here I've just tried to keep it simple), become 3, 21, 24, 37, 39, 42, 57, 66 and 68. Not a bad start.
I've speculated above to potentially trade Bakes. Freo seem like the most obvious one if he chooses to leave, lets say they use Ports or the Pies pick to do so (they won't use their own), that might be Pick 15. Graham moves to Port, they offer him a bit overs so we don't match, lets say we get a 2nd rounder (band 3), that would be Pick 22.
So we now have Picks 3, 15, 21, 22, 24, 37, 39, 42, 57, 66 and 68.
They are a number of teams that will try and trade back to gain more points for their academy / father sons. Adelaide / Carlton / Brisbane and Gold Coast are the most obvious ones currently. Adelaide will either try and trade up (I doubt they will manage to get into the top 5), so will look to trade back behind a Welch bid. Carlton a bit more tricky, depends how the Camp twins go, are they 2nd rounders? 1st rounders? This year will likely figure that out, but lets say we trade for Adelaides 1st.
Thats Pick 8 in my assumed model (based on expected finishing positions - I did a ladder predictor), maybe we trade 15 and 22 for Pick 8.
If Carlton are worried about a 1st round bid for one of the twins, they will likely look to trade back, so assuming Pick 14, maybe we can trade those later picks, 37, 39, 42, 57, 66 and 68 or a combination of them to get it.
Thats only a couple of trades and could leave us with Picks 3, 8, 14, 21 and 24 or something around there. Maybe we could try Brisbane for the other one, or we might be happy with 5 in the top 25 with 2 in the top 10.
It can be done with what we've got and not require us to trade Shai out.