I didn't see this in the long list at the start, so here goes.
My idea for A-Spec mode would be to do away with the preset championships altogether, aside from a few flagship ones (Sunday, Clubman, World Series, etc), and generate ones based on the driver's current car instead.
The available generated series could be given names based on the classic GT ones but wouldn't be set challenges available to all cars. Instead, the opponent cars would be randomly or semi-randomly generated and tuned to match the player's car. For example, not only would they match you in terms of tires and suspensions and power level, but if you were driving a car with stock paint, they'd have stock paint, but if you had a racing livery you'd be against other cars with racing liveries.
You'd be presented with a variety of series available, with tracks and opposition of different levels and types. There would be options ranging from beginner series on short tracks to ones where you could race your tuned car against race cars of a similar performance level on world circuits. Series would be available with tracks tailored to your car type - for example a GT500 car would be able to compete in a series using only real SuperGT tracks, a muscle car would have a series with high speed tracks and American circuits, F1 would have a series with F1 tracks, and a tuner car could enter touge series, a highway series with the Special Stages, or one composed of popular amateur-level tracks like Willow Springs and Tsukuba. Opposition would also be selected by age when necessary, so you could have vintage races of similar cars, or if you drove a brand new DTM car you wouldn't be racing against ones from ten years ago.
The system shouldn't be hard to implement, either - all you'd have to do is add "tags" to the cars that the game would see, with model basics ("American", "Japanese", "Supercar", "Lightweight Sports Car", etc), tuning essentials (RM, custom livery), racing type/series if it's a race model ("GT", "Touring Car", "Endurance Prototype"), age, and even special tags such as famous rivalries. (STI vs Evo, Ford vs Holden, etc). The game could then match you up with cars with similar tags, with various series depending on how many tags you wanted to match. As an example, if you had a modified MX5 ("Sports Car", "Japanese", "Roadster", "FR"), you could have everything from a full-match series where all cars would be MX5s with the same mods as yours ("MX5 Spec Series"), to one where any Japanese sports car of similar performance could enter (So you'd be racing MR2s, other modified MX5s, stock S2000s, maybe Silvias or GT86s), all the way up to one where performance was the only limitation. (With everything from FWD hot hatches to vintage supercars as opponents.)
The system is complicated to explain but would be relatively simple to play. It would allow you to make your way through the game without having to buy or drive cars you have no interest in, and you wouldn't be in a situation where there were no series for the car you wanted to drive, or where you were the only obvious race car in a field of totally stock-looking cars. Seasonal events and challenges could be kept as-is, and would provide options for those who want more traditional series.
A few other thing I'm not sure if made it into the list.
-MAKE LICENSE TESTS OPTIONAL. I'm sure I'm not alone in being incredibly bored of doing them over and over again with every new GT and every new playthrough of the same game. Keep them in the game, let them be challenges with good rewards for winning and available for new players who want an intro to the game, but don't force us veterans to do the same things over and over again to get through the game.
-Multiclass racing, especially in endurances.
-Adjustable ECU/carb tuning. Prioritize power or fuel economy, or be able to choose where in the powerband to make the most gains.
-Multiple engine building routes - maybe we want to do a bottom end-focused build with increased displacement for massive torque, or maybe we want to focus on the top end and rev our car to 11,000RPM. We could still have the same "stages," just let us pick in the tuning menu what we want to focus on.
-Visibly stripped interiors with rollcages. This is a pretty tall order though, maybe only on cars with an RM.