I think your theory may well be correct, and this chap had assets elsewhere. To get a copy of the will, your best bet is to get yourself to the Probate Office in London, or one of the other probate registries around the country. If you can't, then you can send off for a copy, but the postal applications department has been absolutely snowed under since Ancestry put the Calendars online, so they are taking an age to deal with requests. Full information can be found at
www.hmcourts-service.gov.uk/cms/1226.htm.