i've never actually tried discord roleplay — the damn thing eats up my ram to no tomorrow, so using discord at all is entirely out of the question — and i'm quite new to forum roleplay, so i've not a lot of insight on these things. however, taking in mind the strengths and weaknesses of both mediums discussed in the thread, i shall take it upon my humble self to propose a third option. not that i've an ego or anything.
tumblr roleplay meets quite a lot of the 'requirements' you've mentioned, and it's where i hail from in my roleplay journey. i know, i know: tumblr, it's the devil! it's full of far left loonies and is scared of nipples! but, as far as roleplay goes, it's quite versatile as a medium. posts have no character limit, posting times can be as flexible as needed, the available coding seems to exceed discord's (from what i've read)... you can even have your in character, out of character and character sheets all on the same blog, organised by tags. the blogs are also fully customisable, so with a bit of html knowledge you can make a character sheet storage page. not to mention the roleplay resource blogs and countless roleplay pages out there already.
so, if you're alright with deviating from discord, i'd highly recommend it. advertising is easier, too, cause it's all on the same platform. am i blowing my own trumpet here? feel like i am.