IDPA doesn't have a "limited" class. You'd likely be shooting ESP and, as far as I know, as long as it fits in the box and is to weight you are gtg. There are a lot of rules on accepted modifications though so I would read the
rulebook.
You can absolutely use a magwell in USPSA Limited.
ETA: I like SLR. I am not crazy competitive though, I just like running around shooting silhouettes.
I am sure some more hardcore people will have better suggestions.