My sister once had a rustbucket '70s Firebird. The car had a cracked flexplate. At low speeds it created its own sonic boom. At idle it rattled. On the highway it felt lopey, out of balance.

I'd venture to guess that your bolt/nut/washer solution is a contributor to the problem.

Jim's test method is sure and simple to separate engine noise and exhaust noise from driveshaft and axle noise.