I’d add all timewalking dungeons in the same pool and have them up permanently next to normal and heroic (also add mythic +0 while we’re at it) as a dropdown “Random Timewalking”.
Keep the events and add an additional dropdown, e.g. “Timewalking Cataclysm” for people who have favorite expansions.
“Timewalking Cataclysm” and “Random Timewalking” would be up at the same time and could share queue.
I would like to see a better reward system after completing 5 dungeons. I’m often rewarded with something that feels mediocre or not even an upgrade (which is mostly completed on an alt). Perhaps create a cache with options such as the weekly vault. It’s disheartening to spend the time on 5 old dungeons to vendor the cache item for 68 gold. Sigh.
Making timewalking better:
Make a mythic difficulty for every timewalking dungeon season
Make all the timewalking weekly quests give a heroic raid loot box
My thoughts on doing WoD weekly on 3 chars this week, it’s a lot of work for not very fun loot. It would be so much fun to have all those old items available for current season Mythic 1/12. I am so looking forward to farming timeworn M+ when it comes around again, that is my favorite thing in WoW at the moment. I’m still wearing my speed upgraded Arch-Druid’s Tainted Seal on this character, I’m gonna need a big upgrade to retire my last SL S2 Legion M+ item 
Personally the only change I think that needs to occur is a change to the schedule of weekly events.
It should be divided into 3 categories.
PVE: Dungeon week. Timewalking Week.
PVP: Arena Week (Incl. Skirmishes). BG Week (Incl. Epic BGs).
World: World Quest week. Pet battle week.
One bonus should be active for each category.
That way TW is every other week.
PVP-ers always have an event.
And people don’t get disappointed when they log in to see it’s Pet Battle week. I know I’m not alone on this. It’s just a non-event week for me.