This may sound strange but I'd recommend using a character with the opposite playstyle that you use for Toon. There's a couple of reasons for this, one is that you get to feel the game from a different perspective when you're learning the character you choose. This can help bolster some fundamentals that can still apply to Toon that you don't currently use too often with Toon, helping you improve in the process. This could also help you figure out how to better keep this kind of character out if you like to play a zoning/keep-away type Toon.
The second reason is that opposite characters usually don't share the same weaknesses. Characters like C.Falcon or Fox aren't in any way weak to fierce rushdown.
So my recommendations kind of in order from most to least is:
Fox (great areals, properly spacing his smashes and tilts are key, fast faller, fast, rushdown oriented)
Shiek (crazy good arials, properly spacing tilts and smashes are what lead to combo/kills, extremely fast, rushdown/combo oriented)
Diddy (All of his arials [except nair] are equally great, faster than average, spacing Fsmash correctly makes it very safe, has some projectile game to reinforce Toon [peanuts and banana], has a lot of mixup and combo potential)
C.Falcon (up air is so good it's basically all you need, fast, fast faller, properly spacing Fsmash is an almost assured kill, rushdown)