So may I assume that at the moment you don't actually have any of these three marriage certificates? and are basically joining dots based on what you can see listed at the online indexes? Perhaps your assumptions re those dots is correct, but perhaps you should consider validating by obtaining the actual records rather than just looking at the index entries.
Looking at Meddings war records you can see he was not exactly a model soldier and I don't find it odd that he was married during all the things that took place in 1916. I do find it odd that somehow Stuart married Claude Milne while she was still married to him though and THEN that she sailed off to NZ and married Vernon.
When did the MEDDINGS marriage take place? It was registered in the 3rd Quarter of 1916 (July, August, Sept). He was not in England until mid June 1916, and even then he was still serving out his Field Punishment No. 2 (56 days from 5 May or from 17 May takes that into July 1916). This hospital where he was sent for his Gun Shot Wound to his arm was NOT anywhere near Gateshead, Durham.
His AIF records show he was Marched out 28 October 1916 (4th Quarter) , and he notified the change of kin in November 1916. PERHAPS the marriage was 31 Oct 1916 (4th Quarter !) as the AIF records show the nok changes effective date as 31 Oct 1916. If so, how did he get from Weymouth to Gateshead and back to Woolwich, without furlough being logged on his AIF papers .....
Perhaps James MEDDINGS was only in England from mid June 1916 until end of Oct 1916.
It is my understanding that among the many difficulties facing anyone in England in the 1916 was the great reduction in the numbers of local horses, as so many were required at the Western Front.
So what method/s of transport got James Meddings to Gateshead and back ?
What was Stewart's occupation as per that 1916 marriage cert ?
James Meddings AIF digitised papers are 60 pages, so it is possible I have missed the furlough break that would point to opportunity for marriage, or perhaps it was not recorded.
BUT that aside, his signature is available at those papers, and his and Stewart's signatures would be on the marriage record too, so may I suggest you start there and compare the signatures to commence to confirm or otherwise that James Alexander MEDDINGS married your person of interest.
Cheers, JM