Can't help either with catalogue info, the V-CC library site doesn't have any Triumph catalogues from that era unfortunately.
They also don't have a 'Marque Enthusiast' for Triumph cycles at the moment, so I can't put you in touch with anyone on that front either.
Here is a link to a Facebook group over here that might be able to assist in your quest for information:
Here's another link to a site detailing the early history of Triumph:
The first company was started by Siegfried Bettmann in 1886, with funding provided by the Dunlop Pneumatic Tyre Co. Mauritz Johann Schulte became Bettmann’s partner in 1887. In 1888 Sc…
triumphbicycles.wordpress.com
...which may be of interest.
I'm not sure on that headbadge transfer being from that early period that your bicycle clearly dates from; I thought they used brass headbadges early on, but I'm no expert.
Sorry I can't help more.