I've thought about some things to improve or benefit blue a lot. I've even contemplated making a thread like this for a while. Very happy to see someone else took the initiative on it.
So for my ideas:

The most important thing make achievements for Odin, Varis, and WoL to keep that content alive. If nothing else gets changed for blue mage Square please fix this. The fact they didn't make a method for clearing as all blue on WOL was a terrible mistake and a horrible precedent. Memoria has no good reason for blues being excluded. Right now it looks like the exclusion is because its tied to the Bozja quest line but that's horribly stupid seeing as blue mage can't even do the MSQ so we already have to unlock everything on a different class. I feel players are smart enough to figure out doing Memoria doesn't mean we can go into Bozja especially when trying to queue will exclude them anyways so really why was this decision made? All it does is keep Memoria dead outside of the occasional TT farm. Odin is the same way. Blue's revolving around keeping those old EX's alive by requiring no echo is something you need to take advantage of.

Blue deep dungeon like you mentioned. Though I envision just a bit differently. Since we blue mages have so many filler spells but they are all rendered pretty useless for blue content due to the fact sonic boom exists I think a deep dungeon where each level you get a random blue spell would be very fun and fit quite nicely into the roguelike nature of deep dungeons.

EX and Raid staffs - This one I really am baffled is not a thing. Every class except ours gets weapons from bosses and they will even go back a certain amount for new classes to get weapons. Our class has 0 stats related to weapons so there's no balancing needed so it should be a lot easier to add blue mage staffs to the weapon coffers. And since a big part of the experience for blue is getting those ex and raid achievements this would further incentivize people to try them as blue. Also just a real crime every update we only get 2 weapons.

A blue relic weapon - So right now the blue mage experience is pretty much the carnivale, the achievements, and the blue mage log. Now these are really fun to do but some added rewards to further make doing them is clearly a theme I am trying to go for. And I feel a relic weapon where you complete the steps through getting items from doing carnivale stages, purchased from using allied seals, unlocked from filling out the log, and special items for doing the exs and raids as blue to encourage going back and doing them would be really beneficial to the class. And a nice shiny weapon to match the other classes would be appreciated.

Blue Ultimates - seriously please let blues into ults. Blue is the most fun class and I want to see what sort of wild and silly shenanigans we can do in them. Its not like we can do the current ones anyways so the newest ults stay pristine or whatever and you can even prevent totems dropping if a blue is in the party to try and keep the xenolocking thing blue revolves around. Though please give us a blue ultimate weapon. Seriously you guys slack on blue glam choices. I do get that ultimates are very tightly designed experiences of which blues were not factored in nor should they be but at the same time there is 0 reason to not give them the full blue mage party achievement treatment. Yoshi P I am begging you for this.

Blue DRS - I know blues can't do Bozja and they don't fit well with the exploratory content blah blah blah. But I don't care to go into Eureka or Bozja with Blue, though getting to do BA with blue would be fun, we don't need to be let in. However DRS is queuable content. And its hard content. I think being able to do full blue runs with a Mightier than the Queen achievement after would be so sick. And the whole point of this class is to have fun. Make blue not be able to use actions to keep the xenolock and then let blues figure out the rest. Just let us in man.

And finally change the blue update period - So right now we get updated to the previous expansion at around X.45 of the current expansion. This is fine but I propose we change it to X.55 for the update to the current expansion. I know there's all this nonsense about blue being way too strong and while that is true at 60 and below the curve of power is getting closer and closer to regular classes. Now with .55 the current expansion is done. There's nothing else but waiting till the next expansion and a blue update to make all the content you just made fresh again for that down time would be appreciated. It would also just be nice to have a short period where we are on the same level. Where blues can play with their friends on regular jobs on current stuff. Just a little grace period where the entire community is together before the new expansion starts. It would just be fun and the tiers for all the hard content has already been cleared by this point so there's no blue wrecking the difficulty or whatever silly nonsense. It would be a nice way to have fun and send out the current expansion. Plus having to wait to the expansion after to go to the New World with the most New World class is just so freaking lame.

And then some misc things I want. Let blues into variants with the EW update. If we get excluded that will be so stupid, give us spell in waiting really that was like the ShB spell what a crime we didn't get it, another blue mage savage mount like come on that was a good reward for clearing the raid and the every other update would have been a good model for giving us mounts, more than one stage in the carnivale per update I think 5 would be a good amount with the last one being a boss as per usual, some way to set blue mimic type in pf without bosses recognizing them as roles - I realize this may be impossible but would be so nice for making blue parties it would kill the awkward silence phase of trying to see who will tank or heal when making a party with all the slots blue and eliminate non blues joining with the join as role and swap method. But of course blue parties remixing fights due to us being all one role is a crucial part of the experience so I would rather not have this if the only way is to make mimic be recognized as a role. And lastly blue mage lb would be nice. I think level 1 being caster lb, level 2 being healer lb, and level 3 being tank lb would be a cool and thematic way to give blues an lb. We can do everything after all.