This may not simplify your decision, Eliot... *LINK*
David Barnett
...but maybe it'll help in spite of its length.
"(1) that the substrate should be as flat as possible, (2) that the substrate should be stable and something that doesn't flex, and (3) that cast iron was often considered excellent."
(1) Well, things can be made flatter than you might imagine, although past a certain flatness there would be little or no benefit to woodworkers for flattening or sharpening tools. Now just how flat something would have to be to make no appreciable difference is a point of contention, often a seemingly endless source of great delight for some on both sides of the issue, and for others a source of ongoing irritation.
Let's for the moment agree that flat should be affordable, readily available, and, well, flat enough rather than "as flat as possible" which can be relegated to those with needs for far greater precision than we woodworkers would likely require. (I realize my wording borders on nonsensical, but bear with me.)
For me, that would generally mean ±0.001" over the length of a honing stone or lapping plate would reach my limit of acceptability. For other purposes, I'd demand tighter tolerances, but ±0.001" is within reason. Well, I could live with it, but I'd likely grouse about it and if possible, improve upon it.
For others, looser tolerances might suffice. Norton rates their diamond honing stones at ±0.002", which I could not personally accept. Lee Valley allows ±0.005" over the total length of their 8" mild steel honing plates, which is well out of my comfort zone. Fortunately, the LV plates arrive without an abrasive charge, that is, no diamond or SiC grit has yet become embedded in their surfaces, so these plates can be improved upon should one have the means and skills to do so.
At any rate, my advice is to adopt ±0.001" as your target tolerance, which I believe to be a reasonable and affordable expectation for honing stones or plates. For genuine lapping plates, I'd try for better, but that's me, and I'd have little trouble shaving off a few ten-thousandths of an inch and likely have fun doing it.
(2) Things flex, and depending on the area and thickness of surface plates, even granite will flex. But for practical purposes, a thick grey cast iron lapping plate, say 3/4" x 12" supported on another fairly flat surface will factor flex out of the equation. Now 1/2" glass can do the job, but it's more flexible than you might suppose and care should be taken to support it evenly.
(3) Cast iron, especially continuously cast iron such as Meehanite was and still is the standard by which all other diamond lapping substrates should rightfully be measured. I won't go into why this is so, but it is. Let's allow, however, that other substrates are viable (if less desirable), and can be made to work for woodworking tool flattening and sharpening if a) they are sufficiently and evenly flat, b) are sufficiently smooth enough to allow the smallest abrasive particle size you intend to use to do its job, c) are not so soft as to allow the abrasive particles to sink so deeply into the substrate as to be rendered ineffective, and d) are soft enough and the molecular/crystalline structure is favorable to embedment depth and advantageous presentation of abrasive particles.
While the above may be intuitive to some, to others, especially those with little loose grit sharpening experience, it helps to remember that fairly friable stones, such as waterstones, release loose and fractured particles, forming a slurry-swarf mixture that further refines the surface of the tool undergoing abrasive alteration, similar to the lapping process with loose abrasive compound or grit.
Moving on...
"It appeared, also, that granite was good also..."
Granite has advantages of reasonable flatness, ready availability at fairly low cost, especially with the advent of cheap Chinese surface plates, good surface polish, and no real flexibility issues. It is not suitable nor appropriate for abrasive embedment for lapping, however. The advantage of the surface plate is its flatness, stability, surface finish, and in some cases, it's mass. Scratching or abrading the surface of the granite is to be avoided, rendering less than useful for its intended purpose, as a reference tool for flatness and for determining and marking thickness.
It is only lately that granite surface plates have become popular with woodworkers as providing a flat surface to use with intermediary smooth-backed abrasive films, papers, cloths, and so. As inexpensive as these Grade B plates are, I have no problem with using them this way. The trick is to cover the granite surface with the abrasive material to minimize and avoid damage to the plate while accomplishing the intended flattening, smoothing, sharpening, or polishing operation.
One can, for example, temporarily glue a sheet of sandpaper to the plate and flatten the sole of a plane, or affix an abrasive plastic film with water surface tension for polishing a plane blade or chisel back, and so on.
Beyond these direct abrading operations, if the granite surface flatness is maintained and not damaged from abrasives, the surface plate can be used to test and refine a tool, such as a cast iron plane sole, to flatness with a machinist's scraper, a tool that shaves cast iron until the desired tolerance is attained. Granted, this is more of a machinist's operation than a woodworking one, but it is a satisfying and surprising fast way to improve plane performance. Nearly all my planes were flattened this way.
"Perhaps I'll just buy the LV system online and be done with it."
Lee Valley does make a nice cast iron lapping plate that can be used to flatten plane blade and chisel backs. Their new steel honing plates are less flat than I would find useful, but if you were to take the time and effort to improve them slightly, even though they're steel rather than cast iron, the price and ready availability might work out for you. If you use them to mostly do bevel work instead of flattening backs, especially with narrower chisels, these may work just fine for you out of the box. I'll admit I was disappointed that these plates weren't cast iron, but I do appreciate the difficulty of bringing affordable flat cast iron plates to the woodworking public.
One thing, though; to avoid contamination using more than one diamond grit size in your shop, (your being fairly new to this way of sharpening), you might adopt the method that I, Bill Tindall and others have found to be useful. Get a 600-grit diamond honing stone such as a DMT, Norton, or EZ-Lap (EZ-Lap makes a nice long 2-1/2″ x 11-3/8″ x 3/8″, the model 121F for $59.95 -- I know they call it fine, but believe me, it's more medium than fine and more coarse than medium) and use this for most of your bevel work and even for flattening, then use a plate charged with 14,000-grit diamond paste for your final honing. Typically, you'd grind your bevel on sandpaper (ScarySharp), a coarse stone, belt sander or bench grinder, then move to the 600-grit diamond stone, and then finally to the plate charged with 14,000-grit (1μ) diamond paste. Easy, fast, cheap and lasts for years.
"Or better still, stick to my Norton stones and call what I get sharp -- sharp enough."
And as Bill Tindall pointed out in his reply, this may be a perfectly sound solution. If you want to test how sharp your blades are, though, you can always get some 1μ diamond paste, smear a bit on something reasonably flat and preferably softer than a plane blade or chisel, and give it shot. If you're amazed, problem solved. If less than amazed, problem solved.
121F Fine Grit (600) - near bottom of page
