Hi Icrum
Tool rest 1/8" out over 6", that's certainly not a lot, however if it was right on, it would be better. First question what is off, toolrest or banjo, to find out, set banjo at 90 degrees to the lathe axle and measure from lathe bed to top of toolrest, swing toolrest 180 degrees and measure again, no change ?? than it is not the rest, and it could be the banjo, also how much play in the banjo opening for the toolrest, how is the tool rest post, nice and smooth or burred up by the fastener, and what's the toolrest made of, a what I would consider long rest can easily drop by 1/8" on that length if there is some wear, or a combination of wear on the banjo opening and the tool rest post and the banjo bottom. I assume that the rest is still a cast iron one, if wear is the case you could braze up the toolrest post and make it fit better again, if it is a steel toolrest, it would not take much to change the height difference, and if the banjo has worn on one side, that could be rectified by either brazing on some new material or by filing the banjo so it is even again. Also it is very easy to make an other rest, a piece of cold rolled steel and some angle iron, weld it, and you have one, or some other combination of metal, and make some shorter rests while you're at it. If you want to use a long rests I would advise to get 2 banjos and a rest with 2 posts, makes for a much better rest, (less vibration, less adjusting the banjo etc) I don't know what your plans are in turning, but I think the problem of your banjo being off is not a big deal, imagine a 12" spindle you turn that is 1/4" smaller on one end than the other, would that prevent you from working with your lathe ??? of course not. If you where to go and make a lot of dough rollers it would be a pain, but as soon as you make any curves or cut into the spindle to make coves or beads, a concave or convex surface, it would not make any difference to you that the tool rest is of by 1/4" over that 12" length I have a pic. of a tool rest I made and also of one that Leo Lightman made and some other stuff, you can have a look if you like.
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Have fun and take care Leo Van Der Loo