EI-BUD
Personally I agree that a higher profile brand would generate extra traffic for Eastern, particularly if they were to operate as a British Airways or Aer Lingus Regional franchisee. Unfortunately British Airways don't seem too interested in franchising these days (although they do still have a couple in Sun Air and Comair), and I suppose the current Aer Lingus Regional franchise with Stobart might block that as an option. I guess Loganair would be a candidate, but is it really that much bigger and higher profile to be worth a franchise fee.
I notice that Loganair flights from Southampton To Edinburgh and Newcastle are available for sale on British Airways website and app under a BA codeshare (without need for a connecting flight). Maybe Eastern could agree a similar codeshare deal with BA to increase their profile.