I'm really fascinated by your question and suggested solutions. I am glad to hear that you question the wisdom of some of the suggestions. There are a few factors that are important to consider before picking a solution.
What type of hardwood flooring are you thinking of using? Nail down, staple down, glue down or floating? With any type but a floating floor, SLC is definately the wrong product to use underneath, as it will shatter when nailed, and the thinner areas will probably separate from the underlayment when glued to. I also expect SLC will not adhear well to the old vinyl flooring or even the plywood subfloor. Any flex of the plywood subfloor will result in cracks and broken chunks of concrete.
I would explore the possibility of jacking the lower end up one inch. This would of course depend on what type of foundation it is resting on, the roof structure, if the existing ceiling is now level, or does it also slope the same one inch, and finally, if there are any windows in the side walls, as it would effect the level of those as well if jacked.
Assuming jacking is not an option, the next easiest way would be to install "purlins" or surface shim boards every 12 to 16 inches on center across the floor in decreasing thickness and install a new 3/4 inch subfloor over these, screwing it down all the way into the old floor.
The most work, but successful method would be to remove the old floor completely and sister the original floor joists. Using full size sister joists would not be necessary. 2X4s or 2X6's would be fine as long as a good bond was maintained to the existing 2X8's. The custom wedge idea would work fine, but potentially difficult to rip long lengths for each joist and have them all consistent without a good ripping template, but could be done with a little forethought and clever rip guide.
Are the tongues necessary? Can I just take my circular saw right
between the boards, cut them way, and then screw them back down
afterward?
You've been misinformed. The point of tongue-in-groove planking is to keep the floor boards from twisting, slipping and sliding against each other and squeaking (or squeaking more in your case). You still need to secure a tongue-in-groove floor to the subfloor or joists.
Joists almost never squeak on their own. Squeaking comes from two pieces of wood rubbing against each other - usually because a floor hasn't been adequately secured.
Now if you DO need to cut away the flooring, then you should cut along the seams, and then buy Hardwood Floor Spline and rout out the old tongue so you end up with two grooves facing each other, and use the spline to rejoin the flooring when you reattach it.
But BEFORE you do that, I'd get a bunch of 2" coated screws and drop them through the subfloor into the joists below and see if that fixes the squeak. It's subfloor so you don't care about the face, and if it doesn't work, they're easily removed.
*Tip - use a hammerdrill when putting in the screws
Best Answer
Basically you build a new deck on top of it:
In your situation, I'd cut long triangles to use as sleepers, opposed to the shim technique shown here. Subfloor it with 3/4" plywood. Finish with your desired floor covering.
Use a table saw to rip 2x4's; having one end zero inches and the other 2". Install them directly above the existing joists, drilling pockets from the top down if needed, for screws.
Blocking between the joists is advised.
The finished floor will be slightly higher than the adjacent one (that's what thresholds are for), take into account the clearance for any doors that open out, onto it.
If the height discrepancy or if clearance is an issue, you're looking at having to gut the decking. This would enable you to sister to the old joists and bring it up to level, while keeping a low profile.