Should I fix a sloped floor before laying sheet vinyl, and how?

That’s a tough call. While sheet vinyl is very forgiving when it comes to a slope like yours, I would probably fix it anyway. The floor would definitely need to be leveled if you wanted to install ceramic or hardwood. The “how” part is where things get complex.

If it is a single joist causing the problem as you suspect, you’ll need to eliminate that hump first. There are two ways you can accomplish this (check your local building office to ensure you aren’t violating any codes): Removing the plywood and cutting the hump off, or notching/cutting the joist from below to allow it to relax, and then gusseting or sistering that joist with new material to restore structural strength.

Chances are that you still won’t be able to get the floor completely level, even with the above, but if you can get it down to a reasonable amount (say 3/8” or so) you can level out the floor using self-leveling concrete, and then applying a new sub-floor over top which you can apply your flooring to.