I’m not a millwright but my own opinion is this whole dog bone / dumb bell / Rollies dad method / offshoot ‘cutting methods’ is introducing more variables than necessary. The issue is that in order to get any kind of distance between the two reference diameters for an accurate comparison, you will surely exceed the cantilever stick out ratio (call it 2-3 times diameter for discussion purposes). You can’t support the end with tail stock because that introduces a new re-centering variable if the tail stock is out. But you can’t reasonably align the tail stock without first aligning the head stock.
So that’s why you hear some guys recommend a 3” diameter drop of aluminum extending say 10-12” from the chuck. They are counting on the aluminum being lower weight, higher strength & easier to cut so the diameter comparison is more meaningful. Next best might be free machining steel like 12L14. Worse is any kind of crap grade CRS. Real bad is any steel that work hardens like stainless. With cutting you still have surface finish and some degree of tool induced deflection to contend with. Better surface finish = larger nose geometry = generally more infeed force = more deflection. Think about it this way, assume your lathe perfect coaxial to begin with & you cut this same log without tail stock support (which you would normally rarely do). Would you realistically expect the outboard end to be a thou or more larger diameter than the chuck end even after spring passes? The answer is yes btw. Well then you cant assume its cylindrical (equal end bell diameter) for the purposes of head stock alignment. Cutting introduces more variables & like you say, every time you adjust the head stock you have to re-cut the coupon to re-reference the diameters.
Test bars come in a few flavors. They are precision ground to very high tolerance & cost a whopping $50 if sourced offshore. About as much (or less) than the log of aluminum. One type is 100% cylindrical. They are best held in 4J chuck like you did. Theoretically you could have a jaw gripping issue where it is not holding the bar parallel to the spindle axis. But unless it’s badly worn jaws or beat up chuck, that should be minimal. Some folks will say you should never grip anything of precision with jaws like this, only between centers. But I guess just use common sense, don’t gronk the tightening or better yet use brass shim.. This might be a reason why its not as referenced as a standard, even in Internetland where generally anything goes.
Another type of test bar that cuts out the middleman chuck has MT taper on one end and 12-14”cylindrical ~1” diameter section on the other. Insert into the head stock socket, indicate along the cylindrical length. Boom, done. You have eliminated the chuck, related mounting, material deflection properties, cutting forces, surface finish and probably some other things I forgot. If your head stock taper is MT5 you will require the converter socket which hopefully came with your lathe. It does introduce some teeny fit-to-fit tolerance but now we are hair splitting. Either bars can be used for tail stock alignment which is the next very important thing. I kind of prefer the MT style for this reason if you don't already own one of either.
I don’t know but I suspect the suggested cutting methods are related to bigger lathes where they just don’t have access to an inexpensive test tool, so this is the legitimate way to do it. But for hobby machines especially with common MT sockets, it’s a waste of material & time IMO. The cutting method also tells you nothing about an upward or downward pointing spindle or tailstock axis. Yes this form of misalignment has a muted effect on actual taper cutting runout, but again I would prefer to measure it rather than wonder.