My experience with mixing bias rear and radial fronts has been mixed depending on the application. Essentially anything with big tires in the rear and skinny (5" or less) in the front seems to do okay. Not great but manageable swagger. On the other hand putting bias plys on the back of a car with regular size front street tires gets interesting, especially as you start airing them down in the rear. In that particular instance I replaced the front tires with some repro bias plys and the handling became that of a relatively predictable marshmallow. Just how bias ply always drove lol! My advice is to try it for 20 miles. You will know if it's going to work by the end of your test drive. All of my cars are manual transmission so an automatic might provide a little bit different experience.

ps somebody find the pledge to dust this thread off

over the many, many years i have mixed and matched radials and bias ply tires, i have found a lot depends on two things, which really are six things.
wheel base and weight. then mix in skinny[er] fronts and wide[er] rears. add in differing air pressures [F-R] and as can be seen, there is a BUNCH of things boiling down to two differences, the front and rear tire combination on a specific vehicle.
theory may say the "particular combination" will not work, but the only sure fire way is to try it and see. just sneak up on the potential speed of your combination so as to safely learn the particulars of the combination's handling characteristics.

I had steering wandering issues with my old Duster with mix of bias and radials, it was caused by the unknown brand new idler arm wearing out real quickly after I had driven and raced it a very short while
Once I found that out and replace it with another new Moog brand one it was fixed

I am about to find out what it is like with radials on the back and bias in the front on my Barracuda I and putting back on the street...

I guess its a "try it and see" approach?

how much movement do you have laterally speaking? you cant stabilize that much sidewall.. way to much tire for the rim. sidewall steering... a shock change will help but its not the real fix....