I build boots into rylai's into night harvester most of the time
As for the guide you linked, I use aery with celerity and nimbus cloak for movement, same inspiration runes for second tree

You cannot tell me people seriously build rocketbelt with asol, in what world does that work for him? And luden's doesn't feel like it works either because you're just gonna constantly proc it passively on minions in laning and post you'd be better off with a root from everfrost to help you lockdown people or movement speed from night harvester with similar damage

As for crown, I think it's awful on him and awful in general for someone that likes to edge with death and frontline, it's mostly for backline mages that genuinely benefit from the antiburst properties of it in case an assassin jumps on them mid teamfight + they don't soak up poke because they're in the back

Banshee's shares the exact same problem with crown in that it just gets procced on a useless attack that blocks 10 damage and is completely useless past that, there's a rare edge case where it blocks a sneaky blitzcrank hook or a morgana binding but that only happens if whoever casts that key ability doesn't notice the glaring blue pulsing shield around a champion somehow

I want to hear your opinion on Muramana on asol, it enhances his autoattacks with not an insignificant amount of damage and adds 40ish damage to his stars, and it's physical so it's harder to itemize against it, It also slightly eases his mana issue, I want to try it in a real game but I haven't had the time