Is it possible to apply for a visa free transit stamp for a flight with two layovers in China?

My flight begins with a departure from the
USA around 2am on a Thursday, followed by a 12 hour and 50 minute layover in Beijing Friday morning and a 12 hour and 45 minute overnight layover in Chengdu before reaching the final destination in Kathmandu the next morning. I would like to sightsee in Beijing and sleep in a transit hotel in Chengdu.
The layovers are slightly over 24 hours, but the two layovers may be an issue. Please clarify for me.

The return flight has short layovers, I plan to stay within the airport on the way back to The USA.