Thanks for the responses all.

The shoes were, indeed, installed incorrectly. Both leading shoes were on one axle and both trailing shoes were on the other!

I spent the morning taking everything apart, cleaning, and replacing parts. Fresh shoes and hardware have been installed (correctly, I might add) and everything is now working correctly!

There are more issues to be sorted, but for now this problem is solved!
--
http://dylans544.blogspot.com

Since it looks like you may be in the brakes a few more times -

You might use an old NASCAR trick - cover the lining area with a thin layer of chalk -

Then you can assess how much contact area you have between the shoes and drums. Make sure that the shoes fit the drums.

Also, be sure to adjust the brakes before you go for a ride even if you have self-adjusters. Self adjusters do not work that well - it takes several abrupt stops in reverse to get any sort of adjustment. Most people do not stop like that!

Some people have mentioned that the shoes are different - front and rear - and they have put two rears on one side and two fronts on the other. I always mark the shoes as I remove them, and compare new parts with old ones.

I recently read a restoration story where the owner threw the old parts away before he confirmed that the new parts were correct!

What Fred said. Drum brakes are self energizing, the lead edge of the front shoe catches on the drum then pushes the rear shoe via the slack adjuster, that's how they produce good performance without a booster. You have way to much grease too, after you clean and pack the bearings with grease, the rest just needs a very thin coat. Use white lithium grease on the brakes themseves too.

--
69 142S Overdrive + 69 164S Manual

Looking at the picture, it seems like you have two rear facing shoes on the same side. The front or primary shoe should have lining on the entire shoe. Only the rear facing shoe should have the short lining. Hope this helps. Tom

Dylan;

Just some general comments...if shoe tends to relocate up to that position, there must be more force pulling it that way than should be...meaning the force normally pulling it down might be low/missing (Red)...normally up and down pulling forces should be fairly equal (Green and Blue) so that it tends to stay in the middle area (secured by that clip through the backing plate), and doesn't slip of that little "shelf" at corner (Red circle). I'd have a closer look at the way shape at rear of shoe interfaces with backing plate also...is it wrong or is something missing...?

Good Hunting!