Hi Wokauk
I've just recently revived an old ML7 where I found the tail to head stock to be out of line with each other, now I presumed that most of the wear or misalignment would be within the 8" or so from the head stock so I removed the chuck and fitted a small tail stock drill chuck in both tail stock and head stock spindle bore then tightly fitted a sewing needle in each of these, then brought the tail stock up to the head stock keeping a short distance between the needles (the distance really is immaterial at this point) having locked the tail stock at this point I advanced the tail stock chuck with needle fitted towards the head stock needle using the tail stock hand wheel in the hopes these looking through a magnifying glass would now meet point to point, which they did not the tail stock needle passed in front of the head stock needle, which was really obvious when I looked from above, from this I presumed that the tail stock needed adjusting inwards, so I back up the tail stock hand wheel until both needles appeared to be almost touching and adjusted the tail stock adjusting screws, by taking some of the pressure from the tail stock lock and undoing the far side adjuster screw a little and tightening in the front (near side) screw until the needle moved in line with the head stock needle when viewed from above, I re-locked the tail stock down, and check the travel alignment again, at which point the two needles points touch without any deflection from each other, I then screwed back in any slack on the rear adjuster screw, I then released the tail stock lock, moved the tail stock back to allow me now to almost fully extend the tail stock out and then slid them towards each other again leaving the last hand wheel wind to bring the needles together again, which they did. so before I get burned at the stake. the area along the bed nearest the chuck when fitted as far as I'm concerned where most of the cutting tends to take place was aligned head stock to tail stock across the bed at a needle point dead centre to each other, I then without removing the needles, set a cutting tool in the holder to the point of the head stock needle and locked it in the holder, I then moved the tail stock back along the bed ( say 10" or so) and wound the hand wheel back in and locked it down, I now traversed the saddle down the bed to see where the set cutting tip met the tail stock needle, these met tip to point, so that's me happy now to test cut, having refitted the tail stock centre and the chuck. to make a test cut I would need a bit of barstock which could be any length you like 4", 6", 8" whatever of a diameter that could be inserted into the chuck as far as possible to a make clean cut off end and centre drilled as near to the chuck as possible on each end of that barstock, I then extended the bar out of the chuck 1" or so and made a light cut to parallel the bar ends ( to the chuck (material rotation and holding point)), I then fitted that bar in the chuck and tail stock and was able to now make a known test cut at each end of the bar and re-check the cut,
At this point blethering aside I have only used a pair of needles, a Sherlock Holmes (non authentic) magnifying glass and a bit of bar to align, two point about which the bar is to rotate and set the cut height of the cutting tool to cut along between those two points, I found my lathe to now be 0.00025 out of true over the whole available working length of the bed.
In your case widening at the tail stock end would indicate the tail stock needle would need adjusting towards you rather than away (in my case), bed wear this far down the bed from the most used area near the chuck seems a bit unlikely although I'm about to be burned at the stake again, If all the bolts at the motor, head stock and head stock end of the bed are fully secure and belts are running true then the vibration would probably be due to, gibb strip being to too loose in the guide ways of top/ cross and or saddle.
Hope my Blethering helps and I'm certain you'll get any amount of advise all be some of it expensive options.
My ML7 is 1954 fixed to a bit of 2" work top bench and I don't know if that's level so don't get drawn into the spirit level paradox. Try the above which has no real cost first.
Barry (flame on)