How about some sort of "League Recruitment" section applied to the League UI tab when a player is leagueless (and a section to create a recruitment advertisement whilst in one)? Here you can write a brief description of what you are looking for and/or requirements to join, for those that are looking for a league to see what's available. They can then click "apply" (and/or write an attached message) which sends a mail to whomever is qualified (via league permissions) to do so. Just a thought. I know times are tough nowadays.
Not a bad idea, a description would work but to make things easier in addition you could have a checklist of things like casual/semi-serious/serious, when you're usually active, and displaying your Power/CR/SP/Arts. And when leagues reach out to you, it would nice to get a preview of their own league tab to see their members list and activity. Saves a lot of trouble from random ghost invites (which you can turn off thankfully) or when people ask if you are looking for a league.
Now that I think about it, EverQuest 2 (another game run by DayBreak), has a similar feature. Could be used as a good example.
Leagues in general need an entire overhaul imo. The UI, Hall Themes and Layouts, League Hall sized base items, proficiencies, a recruitment centre tab like you mentioned, definitely more base items per room limit, they could set up league tournaments for the nolifers to do and grant rewards ie: most prestige earned, most elite raids completed, league vs league pvp. God it makes me sad at the potential the game has.
Now that I think of it, EverQuest 2 (another game run by Daybreak), has a similar system in place as well. Could be good to base it similarly around that. Idunno
Original EQ has this too. It's been a while, but there were bulletin boards that had guild information on it.