Have you researched Leslies much, in anticipation of your project? Not to get IYF, but from your post, it appears you have not. I am a bit farther down that path than you, so maybe I can be of some help. In no particular order:
Is the amplifier tube or solid state? The L's that have the most cache' are tube powered. In fact, tube power is part of the leslie sound. 35 watts per channel should be fine for a Leslie, esp. if it is tubed. 35 SS watts should do you okay for home or home-studio use, but if you take it on stage with a group, chances are you will be overcome by the drums and guitarist's rig. If YOU are the guitarist, I'd guess you have an amp of 50 or more watts- make your Leslie unpowered, and run it from your amp's powered speaker out. That is basically Clapton's and SRV's approach, as I recall.
A google search will, in time, show you the rotating speed of a Leslie's rotors. Using belts and pulleys, you may be able to get close to one or the other of the "correct" speeds, but as I recall, the speed spread of a L's high and low speeds is much greater than that of a 2-speed turntable, so you will have to be close to one, far away from the other. I can't tell you which you should shoot for, I may have read it somewhere, but I am going from memory- I don't feel my best tonight, so I just don't want to kill myself researching every little detail for you. You will have to do your own scud work!
Your box would have to be mighty tall, if it's 13" on a side, to have the kind of interior volume, and thus bass response, a Leslie cab has. I am talking two stories tall, probably. A L cab is about 3 feet on a side. L's also usually used a 15" speaker (but some did have 12's), so you will probably be disappointed by the bass you would get from your plan.
Also, L's had TWO rotors, one driving a horn for highs, the other driving a 12 or 15 for bass. AND, they turned at different speeds. Wait, there's more. They rotated IN THE OPPOSITE DIRECTION. Some did only have one rotor, but THEY TURNED THE HORN, NOT THE WOOFER- so you are going about this in the exact opposite direction, if you want 'classic' leslie sound. Buying a Leslie horn, either original or repro, will send your project budget through the roof. I have seen a few brave souls make one out of PVC pipe, though. If you want to keep your cab smaller, like you said, I'd ditch the 12 and get a tweeter that has a screw-on horn, or a cheap piezo tweeter, and remove the horn. Have the tweeter fire upwards, into the rotating horn you end up, either bought or built. the 12 is not useless- you can put it in either the bottom of your cab if you make the cab Leslie-sized, or in another cab. Leslies that did not have a baffle for the 12 or 15 fired the woofer downwards, and some had a "Rotosonic" rotor at the bottom of the cab- that was a 15" (or so) rotating drum with a 6 X 9 speaker in it, firing out. Don't bother trying to duplicate a Rotosonic, there are probably plenty kicking around. Heck, I have one I can sell you, cheap.
If you go with a rotating horn and a woofer (rotating or not,) leslies had a crossover, you will need one, too. As I recall, the cut off point for both was about 700Hz- 700Hz and below going to the woofer, all frequencies above going to the horn. Double check that. Passive crossovers with that setting are hard to come by- your only source is probably companies that make Leslie replacement parts. That means pricy, you can probably get by cheaper with an older active crossover.
Another route for your rotator is to find a rotator from a mid-70's and later "Dolphin" class Hammond or other brand of organ from the same era. Most if not all have a transistor tone generator, and are worthless, even if fully functional- and they usually are NOT fully functional. I have one such rotor, with 1-speed motor, that is probably surplus to me, if you want it, PM me. Those rotors had a 6" speaker in them, which was not rotating, only the rotor turned. You might get pretty close to the leslie tone, but I have been told by a man who should know, that it's a crap shoot- you may end up with a good tone, you may end up with something that sounds like a leslie to some folks, but the true cognoscenti will know better right away.
I may have a couple of surplus parts- Rotosonic rotor, rotor from the Dolphin, etc. PM me if interested.