Re: Extending a cantilevered drive shaft.
 

I've plunged (center cutting) endmills straight down on numerous occassions as if they were no different from a drill bit and have had great results. A professional machinist has even advised me to do so (to accomplish what I needed to).

I certainly wouldn't go replace my drill bit set with a set of endmills and pop them in my cordless drill, but I think in the right application there is nothing wrong with plunging an endmill straight down. On those tiny 1/8 and 3/32 inchers, I'd be more inclined to plunge it straight down rather than take a heavy cut from the side in the case of making a makeshift keyway in a bore. I think the endmill would have less chance of breaking that way.

Re: Extending a cantilevered drive shaft.
 

If the space allows, might welding the hubs of the two sprockets together work? it seem that you have the space available to secure one sprocket, but by welding it you could potentially have the teeth of two sprockets on the shaft of one. No idea for sure, but that may work... wouldn't be too much welding to have done.

Re: Extending a cantilevered drive shaft.
 

I was referring to "three-fluted non-centre-cutting endmills" in that post (because that's what I had available in that size). In general, of course you can use a centre-cutting endmill as if it were a drill. Cutting diagonally like that does demand some care (and a hand on each of the vertical and horizontal feeds), but it yields good results. I wasn't advocating a heavy cut, either; quite the opposite, in fact.

Re: Extending a cantilevered drive shaft.
 

You'd have to put a spacer in between to keep the desired distance apart. But yes, welding up the assembly would be a good option, but you'd have to have a way to keep it all lined up (shaft through bores would be the best) and you'd have to make sure it doesn't get distorted (don't heat it for too long at a time and don't cool it rapidly). Once you have those two things worked out, heck, you could even arc/stick weld it.

I sort of assumed you didn't want to weld anything, which is why I posted about drilling and bolting together. But I didn't really base that assumption on anything.

But if you have any sort of welder (you will probably need around 130 amps) then that would definitelty be the way to go. Also, if you have access to a welder, I think it is definitely something a HS student can do. Just take all proper safety precausions and practice for about a whole day first.

I think it better to get that outboard sprocket driven by the first one rather than have another shaft or something. Instead of making the shaft longer, make the two sprockets one. Who cares if the second one is out in the air. As long as it is rigidly attached to the first one, I'd say you're good to go.