Looking at a cub that's experimental exhibition category,
From what I gather it's not a big deal and you just submit a letter every year describing what you plan to do with it and the FAA is pretty lax on the subject.
Anybody here have any input or experience in owning a certified plane that's been moved to EE category?

I currently own one experimental-exhibition bird and have flown several others. They have all been former military aircraft.

Overall it's pretty straight forward. Do you have any specific questions?

It very much depends on what the experimental exhibition operating limitations for that particular airplane say.

Some older operating limitations are very lax and unrestrictive. Some are very restrictive.

The only way to answer your question is to read the limitations on the particular aircraft.

As to how the FAA enforces them, that is a crap shoot. On a Cub, that doesn't draw much attention, it is probably not much of an issue. An L-39 being used at a personal transport, you might have problems.

probably a dumb question, but are you are it is "ex-exhibition" and not "restricted" ? A lot of supercubs and stearmans had restricted A/W certificates when they were made into cropdusters. You can almost always put those back to "standard"

It's a somewhat heavily modified j3.
I suppose my real question is is it feasible as a toy that will go to airshows and stuff but not really do "exhibition". I wouldn't plan to participate in airshows so I'm wondering if thas an acceptable use for the aircraft or if the old faa is going to chase me down and slap my wrist for flying it around.

Painting with a broad brush here.
Restrictions almost always allow flying for proficiency.
You can't get to a show without flying cross country.
So you probably ought to do some cross country flying to keep up your proficiency.

If it goes to an airshow it's being exhibited, even if it doesn't fly during the show. If you park it at the FBO you're just exhibiting it for a limited audience