I'm not a theatre history specialist but I have worked in theatre management and I think I can help a bit. Looking more closely at what I can see in the newspapers, they seem to me to have had good careers and to have been working regularly enough to do OK financially.
Edwin is acting in repertory in classical plays in 1905, then in 1908 and from 1910 to 1914 in Shakespearian repertory companies. These were actor-manager companies, ie the person running the company also acted, and they visited different towns each week or sometimes stayed in the same town for a few weeks at a time. In 1908 he was with Mr Allan Wilkie's company and from late 1910 to early 1914 Mr Alexander Marsh's company.
To give audiences plenty of choice this kind of company presented a number of plays each week, eg in Gloucester in February 1911 in one week 'Othello' on Monday, 'Macbeth' on Tuesday, 'Twelfth Night' on Wednesday, 'Merry Wives of Windsor' on Thursday, 'As You Like It' on Friday, 'Julius Caesar' on Saturday at the matinee and a double bill of 'David Garrick' and 'The Corsican Brothers' on Saturday night! Rehearsal time would be very limited so it relied on experienced actors knowing the plays already, but it was regular work which certainly would have developed and maintained their skills.
After the outbreak of WW1, in late 1914 he was in regional performances of a 'scriptural drama', previously staged by manager Mr Herbert Tree in London. Mr Alfred Denville, the company manager, gave speeches during the interval, recruiting for the army and asking for support for Belgian refugees. In 1916 he and Agnes were in Mr John Carlyle's company as a principal actors in 'Brave Women Who Wait', a play with a wartime theme. After that he served in the war himself, quite eventfully apparently from a newspaper reference later on: 'When taken prisoner, it was wrongly reported that Mr Beverley had been killed, and a theatrical paper published an obituary notice . . . '
He next shows up in Denville's Stock Company in Burnley between May and August 1921 and from April 1922 to March 1923, again with Agnes. Alfred Denville and his companies were well-known. They presented 'weekly rep', performing one play each week while rehearsing another for the following week. Audiences and local critics would get to know the actors and enjoy seeing them taking on different parts. The plays were melodramas, romantic comedies, historical romances, that sort of thing, and for actors it was steady work.
One week the local paper gave brief sketches of the company members: 'Mr Edwin Beverley. Mr Denville's producer: his third season since being demobbed, and ninth engagement, ex Shakespearian actor and author of several pieces' and 'Miss Agnes Gagan (really Mrs Beverley), been with F.R.Benson Companies and Allan Wilkie's Shakespearian Company; last in Burnley with "The Sign of the Cross" about two years ago, and specialises in character studies.'
In late 1923 and late 1929 he and Agnes appeared with Mr Edward Dunstan's Shakespeare Company, which included a lot of Denville actors, and in 1933 they appeared in 'Brown Sugar' with the Denville Players. In 1935 and 1936 he did seasons with Tonbridge Repertory Players, a weekly rep presenting detective dramas and contemporary plays, more steady work. After that there are just a couple of references to him in 'The Frog' presented by Mr Prince Littler in Chatham, a play which had completed two years in London.
I haven't found much about Agnes when she's not working with Edwin, but what there is indicates that she had a good career too. In 1917 she was in a Shakespeare company managed by Mr Leon Salberg at the Alexandra in Birmingham. In 1919 she toured in Mr William Maclaren's Company in 'The Sign of the Cross', visiting Burnley and Derby. In 1926 and 1927 she toured in the Edward Dunstan Company, in Shakespeare plays and classical and historical dramas.
To find out more, try googling the company managers - they worked for some well-known names. It seems likely that The Stage would have obituaries for them - even if only the premature one!
Drosybont