Right now I can either wait in a queue for PvE (for what feels like forever Eldar side) or for normal battle. How about the ability to switch on a queue for PvE whilst waiting for normal battle?

Obviously you don't want players dropping out in the middle of a battle to go do PvE, so the PvE queue can merely search while you're in battle but resume once you're out. Hence if you know there's the possibility of joining for PvE, you can cancel your next battle to go fight in a lair.

Additionally, while players who are searching for PvE are battling, the system can gather up groups of PvE-searching players together and give them the opportunity once battle is over to band together to PvE. While some players may finish their match earlier than others, the queue can inform players who are out first that there are other potential members for their PvE, plus, with such a system in place you'd have lots of potential players waiting in queue at the same time so that you're not reliant on a handful of people finishing their battles soon.

Or the long term solution is to make PvE interesting so more people would que for it

I loik dis. I'd do PvE moar often if'n dat wait toime wasn't so disencouragin'. Currently thar be no reason ta' wait fer PvE dat moight be bugged when I can jus' go inta' PvP and wait less and 'ave less issues