I’m not sure how OF works or how you configure it, but in Todoist I live inside the ‘Next Seven Days’ view, so I never really see any list items that aren’t upcoming. (I assume OF has a one-week perspective option too.)
I put - and put away - my checklists in Anylist when they’re not time-dependent. Anylist was designed for groceries (it’s fantastic for that, actually) but you can manually create any kind of checklist, and the free version is enough for most unless you edit lists with another user or want access to the Mac app. You can easily attach pics to items, so I snapped pics of all the different household items (eg lightbulbs, stapler-sizes, batteries) in my place so I can easily get the right ones when at the hardware store, for example.
Theoretically it would be nice to maintain these general checklists into my task manager but in practice it seems to clutter things up there, and besides, I use Anylist for my groceries so I figure I might as well give it other duties…
I pretty much live inside Google Calendar, and Todoist has 2-way sync so that it places dated/timed tasks into GC, and if I move those while in the calendar the changes reflect back into Todoist immediately. That 2-way sync is even available in the free version of Todoist, by the way.