Is 70 minutes enough for changing planes, customs, and immigration in Charlotte on a Wednesday?

Only if you have unbelievable luck.

That's technically not a legal international connection. Are you able to even book that connection, as normally they won't even let you book an international flight with that kind of a connection time.

We only had 45 minutes landing in CLT from SXM (approx 6 pm) on the way to Tampa as we were delayed by about 30 minutes (on a Friday.) It only took us 15 minutes total between Immigration, picking up luggage, going through Customs and rechecking luggage. We even had time to grab a quick meal! I was very concerned, but it worked out great!

Best response to your question is "it depends".
1. Number of international planes landing before during and after your plane arrives.
2. Check baggage or carry on only?
3. Delay time of departure in SXM.
Not sure about minimum layover time for international air travel but I thought it was an hour which would mean 70 minutes meets the requirement.
4. In your favor is that Wednesday normally means lighter traffic and faster C&I than Sat/Sun.

Last time we flew in to Charlotte on a Sunday night and cleared customs, baggage claim, and rechecked our bags in 40 minutes. The new kiosks have really helped speed things up. Plus the Global Entry helped us through the recheck security lines.