In 1929 Ford outsold them Chevy boyz but by 1931 Chevy outsold Ford by a margin of 3 to 1. A lot has to do with their basic construction, ...and it is my personal opinion that it also had some to do with the 'socio-economic structure' of those who owned that car.
To start with, generally the '28-'31 Chevrolet was perceived to be better constructed than its counterpart (the Model-A). Not so much in 1928 but definitely by 1931. If you have ever ridden in or driven a 1927 Chevrolet, ...and in a 1929 Chevrolet, you will quickly realize what I am saying. They were a heavier car that arguably had a better suspension (4 springs vs. 2), better steering, and in the case of the 1927 Chevrolet, they had 3 speeds in a selective-gear transmission vs. a band controlled planetary transmission. I could go on with the differences but the coachwork itself was also something that was much more substantial in the Chevrolet. In 1929, Ford found himself competing against what many buyers considered a better engine (6 cylinder) that obtained better fuel mileage and was much smoother in operation. Likely it was something new that folks had to 'warm up to' at first, but like anything new, once it had been proven it was accepted. My father owns a 1931 Chevrolet Landau Phaeton which was the direct competitor to the 400A Convertible Sedan, and when I compare the two vehicles' construction both in mechanical and coachwork, there really is no comparison. Also, GM had more flashy interior selections with the same being said about their exterior colors.
The downside to Chevrolet was the very thing that made them noteable in that the coachwork over time would deteriorate. The two other things that I think sold Fords was the vast dealer network that he had, AND that he provided in-house financing. He offered a car that folks could afford, ...and saw to it where they had a way to buy it.
Where this socio-economic thing comes into play IMHO is automotive engineering was advancing at a high rate back then. Taking a Ford for example, if you purchased a brand new Ford in 1926, you got a 22 horse vehicle with a 2-speed planetary transmission that many considered underpowered. Three years later, you purchased a 1929 Ford that still had a 4 cylinder, and three years later you purchased a new Ford that could have been equipped with a V-8. The horsepower doubled (as did the speeds) each time you purchased a new car, ...all of this within a span of 6 years. My point is that a 5 year old Ford back then did NOT have any re-sale value because it was grossly outdated. Therefore the majority of people that bought the 5+ year old Fords were folks that could not afford anything more modern. Because of the vast amount of T's & A's that were manufactured, parts were abundant allowing the Model-A to remain usuable through out the years and not become extinct.
So like you pointed out, too much wood which may be considered a design flaw by our standards is where they likely met their major demise. Then poor repair parts availability sealed the coffin so to speak.