So a relatively large investment later...
The talent cell battery is part of the problem. A new LiPo 3.7V battery and a reconfiguration of the circuit has helped. The direct linkage of the battery to the GSM 1400 (using the standard 2-pole JST connector) and the utilisation of Vcc did not work. The current draw appears to be the problem as identified by panda in the thread in the earlier post.
I haven't tried the capacitor option but don't need to now as the prototype is working.
Thank you Pert.