The worst mandolin I have for changing strings is a National RM-1 and the best way to do it is to use a blob of Bluetack and a capo - I assume this would also work with a Gretch.

Most mandolin tailpieces have their faults - try getting the strings "off" a Collings Mandola! Anyone thinking about better tailpieces should investigate the "James". Problem is they cost almost as much as most people are prepared to pay for a mandolin