David, yes an EL34 should normally sound more upfront and sunny than a 6L6. 6L6 generally sound more lush and romantic, which many prefer in this day where components run more forward and/or lean even if today's high-end audio tube amplifier manufacturers rarely employ it.
You might want to give your Shuguang EL34 a 50+ hour try out. I find Shuguang tubes quite underrated, perhaps because of their low price. In my experience, their standard 12AX7, EL34, KT88, and 5AR4 represent the most rugged current production tubes. So, I'd have no fear in swapping them in place of the EH.
As you mentioned, some JJ variants do have a somewhat deserved reputation for failure; the E34L included. Still, I would not worry about yours since they test well. But again, try the Shuguangs first, and see if they begin to step in the direction you are looking to move. The JJ E34L will not sound as full or as even handed from top to bottom as the Shuguangs, but often present a more notable midrange.
I didn't live with Gold Lion KT77, but they're a tube to consider. I never liked the JJ variant as much as most did when they came out. Depending on the amplifier and system, I prefer either the JJ EL34 or E34L, but their KT77 always places third in the race. I have a quad of the big bottle 6CA7, but haven't tried them. I do like the EH 6CA7 tremendously, even though I have a pretty strong dislike of most (too harsh) Sovtek and (too muddy) EH tubes.
Again, I don't know enough about your amplifier to determine how it reacts to its output tubes...
