72 Hours Transit Visa By Boat/Train?

Hello,

My girlfriend and I are from the UK and wish to take the Trans-Mongolian train from Beijing to Moscow in March 2015 after crossing The Yellow Sea by boat from Incheon to Tianjin.

Our ARC cards expire, however, on 4th April 2015 so we have less than six months validity left on them. I believe this means that we cannot apply for a standard tourist L, so, I was wondering - can you transit through China to another country (in this case Mongolia) for 72 Hours by Boat then Train?

If not, is there a different type we can get (like a seeking work Z type?) that is not linked to former ROK residency and ARC validity? If so, can we apply for this anywhere in Korea (I saw something about Busan)?

If none of these options are available - can we send our passports back to the UK and get a Chinese permit that way (so that it is issued irrespective of the time we have spent in ROK)?

Thank you so much in advance for your help.

Daniel