Your information is incorrect. It is well known and documented (TIMATIC, PRC consulate web sites, and official legislation from Beijing) that TWOV passengers are allowed to leave the airport.
Also, someone else mentioned that DL's "China reservations desk" is better than the US desk. AFIK, DL does not have a China reservations desk; all calls get routed to Singapore, BUT, if you call the people in the BJ, SH, or HK offices directly, you can often get those people to help you, and I agree that they are far better than the call center agents (in both the US and Singapore).
If you follow this link:
You get these details which would seemingly conflict that TWOV allows one to leave the airport:
Transit Without Visa (TWOV): Passing through an international
transit area of the airport in order to board a connecting (or
to proceed by the same) flight, without entering the country
(i.e. clearing immigration).
Unless stated otherwise, passengers wishing to TWOV must:
- be en-route to a third country (e.g. itinerary TYO-LON-TYO
is not considered TWOV);
- prove that they will continue their journey within the
prescribed period (e.g. hold onward tickets);
- have documents required for entry into the country of
destination and for transit through countries en-route;
- remain in the transit area (airside) or on the aircraft.
Baggage belonging to TWOV passengers must be checked through
to their final destination.
TWOV is not intended for those holding stand-by tickets, e.g.
airline staff or other passengers travelling on industry
discount.
Nevertheless, we're gonna go for it - the consulate said visas were needed but why not try? I spoke with China Southern and they confirmed that it's up to local officials and cannot be guaranteed, but is not usually denied. They forwarded me an application to print out and bring with our passports that is a visa waiver form. It has worked for others so hoping it works for us!