Is it possible that Walmart did not make a lawful stop?
I don't know. You listed 2 states and the laws regarding this are state specific.

I will say this: most states do not require the thief to actually make it out the door with the loot. Many allow you to be stopped for simply hiding the merchandise on yourself, like a thief would.

Is it advisable to call the store back and offer say $2000 in restitution or plead with them to drop the charge?
You can try but if they were going to do this, why call the police at all. There is likely a bill for a civil forfeiture headed your way. Again, state specific so I cannot look up the amount they can charge but I have seen it as high as 10 times the amount stolen.

any advice would be highly helpful.
sure. Take that $2000 and add another 2-5 thousand more with it and hire yourself a good lawyer. Given your history, that is about the only way you are getting anything reduced.