Pushing tension is compression. Turnbuckles aren't designed for that, the rods and/or the turnbuckle will buckle under load. In tension they stay aligned and can take a lot of load, but not in compression. Bear in mind that the compression load on it will be something like 2500 lbs vertical during a bump load event so if you can keep a 45 degree angle it will see about 3500 lbs of compression. The more vertical you can keep it the better.
If you want something adjustable you'll need a jackscrew of some type, which has much heavier parts in it and fittings that are designed to keep everything aligned to prevent buckling. If you don't need it to be adjustable maybe just get a bracket welded up with a box tube extending down from the axle mounting bracket to the axle. Then through bolt the tube to the clamp set up you're planning at the axle end.
Good luck!