If you make drop rates normal, and increase instance timer to 1 week, you can still spend the same relative amount of time (in terms of length) farming (1 month ish) to get at least 1 piece of your gear, and possibly additional pieces.

That's what WoW does. Instead of punishing people who can't do the same raid 10 times in a row each day to even get a shot at drops, they make the drop rate normal and extend content by increasing instance timers.

I think a system that actually drops the items without needing to spam it, is much more amenable to a player in terms of fun and replay factor.

Requiring a speed run to get chests is also silly. I think it's fine for Relic items, but not really as a limiter to what a group of people will get to experience/obtain