If it were me, I would go with radials if I didn't want or expect that I would ever wan the car to be judged or that it would otherwise score well enough that the 16 points(?) off the top would'n matter that much. If I did want it to be judged and the points off would be devastating to my pride, etc, then I would get as close to the size as was available for the car as offered by the factory back when it was built. It would be as simple as that.
As to the harder steering owing to the tire's footprint, just practice turning the car while it is in motion rather than static. Generally he more the front wheels are moving/turning relative to change in steering the less the effort needed. Yeah, I know, that's a no brainer also.
I think Coker makes/handles several options in either bias ply or radials. The good stuff costs more just like it does for anything else. So bite the bullet, raid the misuses
pocket book, sell a pig or two and do whatever you reasonably can to satisfy your mind so that afterwards you have no regrets. Remember: when it comes to pampering our old Chevrolets, money is just a detail and pride in it is everything Is too!
Best,
Charlie
BTW: As to 37/38's steering hard, well ... What, can I say. Maybe you should have test driven the car before buying it. I sure do feel your pain. Not really.
BTW2: Important: Put the money back in the missis's
pocket book before she discovers her "mad money" is missing. Being nice to her for a change may extend the span of time before you screw up again and she decides to go shopping while experiencing the instant "hissy fit." You know.
BTW3: Do not show or mention BTW2 to the missus.
Doing so will show your hand and you may regretfully experience life out there sleeping with "Rover" for quite some time. Generally, "Rover's don't like to be cuddled or sleep in the "spoon" position. Just saying. You've been warned.