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.
I think the word is actually spelled "purlin," and normally refers to framing members bridging laterally across roof trusses, rafters, or wall posts or studs.
You say (in the other question) that the slope is consistent, i.e. the floor is still planar, just not a level plane. This means the method suggested by shirlock homes in your other question shouldn't be too difficult; certainly a lot easier than the other options you mentioned.
If the slope is across 10 feet, and the outer edge is 1" lower than the inner edge, you'd start by ripping a 1" strip off the edge of a piece of 2-by lumber, so you'll have a strip that's 1" x 1.5". Attach that to the existing subfloor at the outer edge. Now say you've decided to put these shims every 12", that means you'll end up with 10 of them across the 10' dimension of your room, and each one will need to be 1/10" shorter than the last one so that you end up at zero right where the room meets the house. So rip your next one to 0.9" thick, or about 29/32", and attach it parallel to the first one, 12" away from it. Next one will be 0.8" or 13/16", and you'll attach it 24" away from the first one. Then just keep going until your last shim is 0.1" or 3/32" thick, and it will be about 12" from the inner wall of the room.
Once you've installed these shims, their top surfaces will form a flat level plane onto which you can attach your new subfloor. Your finished floor will be higher with this method (at the threshold it'll be equal to the thickness of your new subfloor plus the thickness of your new flooring material, and at the outer wall it'll be one inch thicker than that), but if that works in your situation I think this is a great solution.
Best Answer
The common tool to do this is a level. One that is 4 feet long is better because it can check the floor over a wider area for flatness and level. You really only need to check the area where you intend to set the book shelf and not the whole room.
A level like this would not be considered an advanced tool as they are rather simple devices. If you find the longer sized levels too expensive you can instead find cheap short ones that you can use on the top edge of a 4 foot long, straight and even pine board.
If you want to avoid buying any tool at all you could consider the idea to use pine board like the above example but substitute the cheap level with a Smart Phone running an app that simulates the bubble style level. For example there are many apps like this in the Google Play store for Android phones. (Similar apps on iPhone at the iTunes store site).
The smart phone apps require you to calibrate your phone on a known level surface. Some folks may consider this idea a gimmick but it may be just what you need for a quick and simple check. The quality and repeatability of the cell phone type of app can vary from app to app and be affected by the quality of sensors in the phone. So if you go this direction I encourage you to download three or four of the free apps and find the one that best suits your needs.