Hey Mike, you do understand the situation! To answer your question about how I determined the 0.005" of tailstock offset, here is what I did. After obtaining the very good headstock to lathe bed alignment, and verifying it by chucking a 5/8 brass bar stock to near zero runnout, I took very light cuts at positions near the chuck and at 5" plus out from the chuck.. Then measured and compared. (I obtain the initial alignment using a ground alignment bar that fits the Sherline morse taper in the headstock. I indicate back and forth from the carriage the vertical and horizontal.
Okay, I think I get it. You aligned the headstock initially with a Morse Taper ground test bar, then took two test cuts on either end of a brass bar and measured the difference, then adjusted it until you got 0.0005" over that run, correct? Not a bad way to go but let me tell you how I do it. Maybe you might try it.
I don't have a MT bar; I just center the headstock in the middle of the play the key allows. I use my 3 jaw chuck to chuck up a piece of 8mm ground rod from a discarded printer. This stuff cuts like butter so its good for test cutting. I use a piece that is about 6" long and put about 1.5" of it inside the chuck jaws and lock it down. This leaves about 4.5" sticking out. I then take a very sharp HSS square tool and take two 0.005" cuts from the end toward the chuck, stopping about 1/2" from the chuck. Then I crank up my speed to about 2500 rpm and take a 0.002 - 0.003" deep cut the entire length of the rod. This gives me a nice finish that I can measure accurately. I adjust the headstock until I get zero deviation at the end, the middle and near the chuck. It doesn't take long to do and the stock headstock key provides enough room to get the headstock aligned. I do it this way because I prefer a cutting test that aligns the headstock in the position in which it is used. I figure if I can cut a taper-free work piece, unsupported over a 4.5" length, then the headstock is aligned well enough for me. A 2-collar test is good for leveling but it is not so good for headstock alignment.
Ok, then held a dial test indicator in the headstock and used it to indicate the tailstock. I indicated the OD and the ID of the tailstock. I also indicated a dead center in the tailstock. All readings indicated that the tailstock was positioned .005" off horizontally. It is indicates to be about 0.001" low. It is the horizontal offset that bothers me the most.
Okay, I understand what you did but it is not accurate enough to quantify the tailstock offset. You need to make a test bar.
Find a piece of steel about 10-12" long. I prefer O-1 steel but any steel that will give you a decent finish will work. The OD should be about 3/4 - 1" OD and you will need a 4 jaw chuck and a steady rest. Chuck up the rod and dial it in near the chuck. You can temporarily support the far end with the steady rest until you get the part dialed in to zero at the chuck end. Once you do that, slide the steady rest up close to the chuck and bring the arms juuust into contact and lightly snug them down. The slide the steady rest toward the end and dial that end in to zero with the arms of the stead rest. Once done, face the end of the rod cleanly and center drill it; a sharp #2 center drill works. Now flip the part over and repeat to center drill the other end. You now have a short rod that is center-drilled on both ends that you can put between dead centers. Attach a lathe dog on one end and mount the work piece between centers. Move to the tailstock end and take two 0.005" deep skim cuts X about 1/2" long. Then take a 0.003" deep cut with a slow feed to produce a fine finish. You have just made a lathe test bar that is a precision instrument that you should treat with care. It will work on any lathe.
Now, mount the test bar back between centers but with the turned end toward the headstock. Use a dial indicator mounted in the tool post and be sure the tip is on center. You are contacting the work piece on the turned section of the rod. Preload the indicator by about 0.015" or so and zero the dial. Now, without moving the cross slide, back off the tailstock ram and flip the test rod end for end so that the turned part of the rod is on the tailstock end of the lathe. Tighten the tailstock ram just enough so that you can turn the test rod with a tiny bit of effort; this assures the centers are fully engaged but you aren't using enough pressure to bow the rod. Now lift the tip of the indicator away from the rod and move the saddle toward the tailstock until you can put the indicator tip on that turned section of the test rod and note the reading. The difference between the readings will be your tailstock offset. Do this several times to make sure the readings are repeatable. THEN you can decide on the magnitude of the problem you have, if you in fact do have one.
I have watched the Brazilian youtube video on making the tailstock adjustable. I have the Sherline tailstock chuck adapter, and I can center it. But, I really dislike using it and it does not help if I want to turn between centers. I don't want to buy another adapter just to be able to true up a tailstock center.
I have found that the A2Z company USED to make an adjustable tailstock using the Sherline milling machine tailstock. Problem is that A2Z is no more, otherwise I might try their solution.
Your point about the stud that is used to lock down the headstock might present a problem is noted. There is only about 0.003" clearance in the stud to headstock, but the stud does have some wiggle. The offset key may or may not work. Just thought I'd give it a try before butchering the tailstock?
Let's wait until you quantify your tailstock offset. If it is excessive then maybe we Sherline guys can brainstorm and figure out a solution that is acceptable to you.
How about selling me that nice Emco Super 11?
NO!