I would have thought it was normal for a single ball race engine to have some fore-aft shaft movement.
In TBR engines the lack of movement is due to the locking the front race onto the step in the shaft and the outer races being a controlled distance apart dictated by the case machining.
I don't think it's good practice to lock the shaft itself to the inner race by tight fit and its would not be necessary to lock it in with Loctite either.
A bit of fore/aft movement does not do any harm, provided an electric starter never gets near then engine (banish the thought!).
The Irvine Mills will not ask very much of any bearing, anything the right size should do, but I suggest it should be open or shielded, and NOT sealed.
Playing cards make good gaskets around 15 thou'.