Ok, first you are using an unsafe floor jack with no pad and the wheels will not move when rusted. Way unsafe. You are asking for a problem with that floor jack. You should not be lifting this with a jack like that. You ask for safe procedures and then you show the messed up floor jack. Get that out of there.
Second, inner parts of the tubes, where they come out of the diff have enough room where the sway bar bend is to allow for the stands to be placed as I stated. Or at the very ends of the tubes where the sway bar ands may allow enough room. If none of this works. Spread the stands out to the ends and set the sway bar itself in the curved stand arm saddle. Or, set the rounded part of the sway bar attaching bracket in the curved saddles. If the sway bar is directly below the axle tubes, setting the stands under the sway bar or the brackets, will not hurt it. If the sway bar is offset and is either forward or backward of directly under the axle tubes, do not sent the stand saddles under the sway bar.