Check if the floor is level before installing new linoleum (from a roll, not tiles)

I would cut the bottom of the trim so the tile can slide underneath. Then you only need to approximate the shape of the tile, but you don't have to worry about perfect edges.

I've used the Dremel Multi-Max with the 3/4" flush cut blade to cut base trim and door jambs so I could slide hardwood flooring underneath. I borrowed a friend's and decided I needed to buy my own as soon as my next project came up.

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.