Trinkets makes sense next. However, I think competitive needs to have the rest of the trinkets available to pvp and wvw. Maybe weapons too using the mist weapons as precursors.
We really should be able to access all Strikes from any hub. The UI team just doesn't want to take the time to make locks that prevent you from accessing strikes you don't have expansions for.
Interacting with a lantern doesn't dismount you and you can move away while it charges up the lantern to still qualify. Just don't use any specific skills that interrupt interacting.
If you get the bow before unlocking the W3 achievements, then you are locked out of them.
Creating a new character to start over and get all the unlocks is not a reasonable option.