Given their veteran and contract status with the team, its really safe to assume that Perreault, Buff, Slater and Thorburn are guaranteed spots. That leaves 2 open roster spots plus one forward in the press box - so a total of 3.
These are the guys competing for those spots:
Tangradi (1 way)
Peluso (1 way)
Halischuck (2 way) *200,000 AHL Salary
Galiardi (2 way) *200,000 AHL Salary
O'Dell (2 way) *100,000 AHL Salary
Klingberg (2 way) * 75,000 AHL Salary
Petan (ELC)
Ehlers (ELC)
If you're like me and you don't think the Jets enjoy burning money, then that means that Tangradi and Peluso will likely take up 2 of those 3 spots (assuming they aren't traded)
That leaves the other 6 to compete for the remaining open spot. Who wins?
Of course they don't like "burning money" but your assumption appears to be that it is nothing but money. In that case it is the cheapest one. It will be Klingberg. Others need not apply.
I think you unfairly overstate the influence of contracts on this process. They all require waivers except the 2 ELCs. I'm guessing that at the season opening cut down deadline the teams are all concerned with getting their own rosters in order and there is a glut of players on waivers so most or all of them clear waivers so that is not a factor. If Mau wants to keep O'Dell and cut Tangradi they pay both NHL salaries = 1.325 mil. If they go the other way to save money they pay 775k. A difference of 550k. Big money to me but I hope the Jets are not so cheap as to make roster decisions based solely on that.
Tangradi (1 way) 675,000
Peluso (1 way) 562,500
Halischuck (2 way) 725,000 *200,000 AHL Salary
Galiardi (2 way) 700,000 *200,000 AHL Salary
O'Dell (2 way) 650,000 *100,000 AHL Salary
Klingberg (2 way) * 75,000 AHL Salary
Petan (ELC) 692,500 + PB 232,500
Ehlers (ELC) 925,000 + PB 575,000