If you alter the Main Race mode like you suggest, it would simply be an alternative Battle Race. Wouldn't it be better to just fix Battle Race by either adding multiple lives or to simply no longer lose the upgrades if you choose to continue?
That would work fine too. But I guess my suggestion could be easier to mod, since you wouldn't have to change the rules of the tournament and etc.
Also, I think that just in the Hard Mode of "Main Race" you'll be able to race in all the stages of this game.
You would just have to see what vallues are different in the races of "Main Race" and of "Battle Race" and copy and paste, I guess.