Jackshaft Installing Jackshaft into Bicycle Crank Case?

RocketPenguin

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Bought this great bicycle off of Craigslist for a whopping 10$, with everything working. The last owner road it to school and back every day for a year (2 miles there, 2 miles back) and so of course, the tires are worn, along with the front crank (Dunno about the rear hub, haven't looked at it yet.) The crank wiggled a lot, and as i decided earlier to use it as a jackshaft, i changed my mind. Taking it apart, i find that the center axle is worn, the bearings are worn, everything is worn, one side isn't lubricated, etc. End up taking the whole thing out, seeing as i no longer can use it.

Now the question is, how would i go about installing a jackshaft into the crank housing? Buying a new bicycle crank would be pointless at this point, as you can't mount sprockets onto them without modding, and plus, they aren't made for 4000+ rpm. It being in the perfect spot (Engine fits perfectly right above it) i don't want to attach a jackshaft elsewhere when i already have a great mount position for it. So, question is, how would i mount a real jackshaft in there?

I was thinking this:
I still have the two caps that thread into the housing, and so i was thinking, first start with lathing out the center to accommodate the new axle. Then, snugly fit a ball/roller bearing into the housing, followed by a pipe that has the same OD as the bearing, followed by another bearing, followed by the other end cap. This would leave two bearings sandwiched between the two end caps, with a pipe as a spacer to keep them farther apart. In order: Cap, Bearing, Pipe spacer, Bearing, Cap.
This whole thing would be held together by the two endcaps screwed into place.

Would this work? Any better ideas?
I can have dimensions tomorrow.
Also trying to keep this semi cheap (Preferably the whole jackshaft including axle under 20$)
And what size of a axle should i use?
 
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