[Marshall V. Daut]

Tire pressures checked out o.k. Good! Scratch that from your list of potential troublemakers. $10 down and we move on to Bennett Cerf. (Remember that catch phrase from the 1950's "What's My Line?" TV panel show?)
There were a couple different rear springs installed in Model A passenger cars, depending upon the body style and application. Of course, the heavier bodied Model A's received the heavier duty rear spring with 10 leaves, #A-5560-D, meaning mostly the Fordors and Town Sedans. The Tudor Sedan's rear spring also had 10 leaves, #A-5560-A. Even though the Tudor and Fordors/Town Sedans both had 10 leaves, there must have been a difference in spring tension, as the Fordors were a heavier car to start with and conceivably could carry more passengers than a Tudor Sedan because of the bench front seat. If both 10 leaf springs had the same resistance, Ford wouldn't have had two different part numbers. By comparison, the roadster had only 7 leaves (plus a dummy leaf on the bottom), followed by the various coupes with 8 leaves.
If your car had been restored by someone else from a pile of parts or a different rear end w/spring was shoved underneath your frame, it's possible that the wrong spring is in place. This wouldn't be as noticeable with only the driver or with one passenger seated up front. But put a couple adults in the rear seat - especially rotund adults - and the rear spring with either too few leaves or the wrong resistance will compress, lowering the rear end and raising the front end. This will cause weird steering and handling characteristics for sure!
Even if your spring has the correct number of leaves and is in fact an A-5560-D spring, it may be fatigued and no longer able to support the weight it was designed to carry. First things first. You should be able to determine the number of leaves in your rear spring by counting the visible ones beneath the rear crossmember and then feeling up inside it to count the shorter leaves up top. If you have less than 10 leaves, this may be your problem. Coupe springs with 8 leaves are very common. But even if there are 10 leaves, who can say if the spring is fatigued or if it came from a Tudor Sedan? Fully loaded, does your car squat in the rear with a commensurate lifting of the front end? The car should remain almost level fully loaded, or only dip down in the rear slightly.
Check out the number of leaves in the rear spring and whether the car squats in the rear when loaded with passengers, and you may have found the cause of the problem. If this began happening only recently, I'd say your rear spring has finally given up the ghost and is sagging when over-burdened by the extra passenger weight. A new correct resistance rear spring for a Fordor ain't cheap, but it will make a world of difference if you have the wrong spring or it's dead. Not much point in owning a Fordor Model A if you can't haul passengers around seated in the rear!
Marshall