Hot Rods Early Ford banjo rear, is this axle bent? Options?

Has to be an issue in the tapered hub area
Maybe it’s been flogged out at some stage , if the hub/bearings are ok there is no other way
Oh and it’s way to late on a Saturday night and l have had way to many scotch’s but curious to see what you come up with
But yeah as has been mentioned get in there and pull the hub off
At the very least you’ll get to see the condition of the brakes and bearings

 

When you get the wheel puller remove both rear wheel brake drums
and compare them. Also, switch the brake drums from side to side, rotate the wheel on each side and see the differences, if any. A '40 Ford hub is shown below.. Also, the 40 outer rear axle wheel bearing does not fit tightly against the axle. In second photo the grease seal has not been installed so you can see the bearing.
Take a measurement from the inside machined surface of the hub to the inside dia. of the brake drum where the shoes make contact to check for concentricity.

 

Well, if it is a bent axle, it is no good the way it is. You sure as hell can't hurt it trying to straighten it.
Get the axle out. Put it in some V blocks and indicate the axle for straight. Straighten accordingly.
I wouldn't hesitate. I'm pretty good at straightening out bent **** after decades of dirt track racing Sprints and late models.
I just remembered an old trick for checking for a bent housing. Probably not your problem, but easy to check. With rear end out of the car and both tires and wheels on, make a mark on top of each tire and measure the width. Then rotate the axle housing, without rolling the wheels, 180 degrees from where your first measurement was taken. Now measure the width again. If there is a difference, the housing is bent.

 

Maybe you bent/twisted the axle by drag racing.

 

So I watched the video, my non expert opinion…

The bearings ride on the housing if memory serves, the hub/drum go on the taper fit of the axle and the inner hub rides on the bearings. If the housing was bent, the wheel wouldn’t wobble, but the car could “dog walk”. Even if something goofy occurred with the bearing surface or the bearings, pretty sure there would be a pronounced indication, like driving with a flat spot on a tire. the video doesn’t show that, just a wobble.
I’m sure it’s just a bent shaft.

 

I had a Mopar 8.25 rear end with 4.11 posi. I ran it for several years in several different cars. Burnouts, drag strip, daily driver, etc. Wasn't until I put it in my '24 Dodge fenderless roadster that I noticed the left rear wheel wobbled. Found I had a bent axle for years and never saw it until on a fenderless car. Swapped the axle and it's good to go. I would change yours when you can but probably would run the race even so.

Dave