I see you have been down this road, and already know about the soldier who died 1915, his entry in the Effects register, etc:
http://boards.ancestry.com/localities.britisles.england.war.general/8427.1.1.1.1.1/mb.ashxAnd there is compelling suggestion that the
Ernest Albert BOOTH age 22, father named William John, who married Hannah SHAW in 1908 in Birmingham:
https://familysearch.org/ark:/61903/1:1:NXR5-LZY....is the same Albert Ernest BOOTH, b abt 1887, father William Henry who married Florence N PLIMMER in 1914. That is to say, possibly he married Florence whilst Hannah was definitely still alive . Looks very like Florence N. remarried in 1918 under her maiden name.
Have you considered obtaining the marriage certificate of the BOOTH / SHAW marriage to compare signatures perhaps, or look for other clues to prove or disprove the bigamy theory?
Cheers
AMBLY