I have noticed a weird looking pattern after taking a test cut on this piece of 2.5” 6061. It kind of looks like a cross hatch pattern. I suspect worn spindle bearings are the cause but would like opinions from others. I purchased this lathe thinking it was gear noise but now I’m not so sure.
I can't tell you which item it is, but some items there are getting into a harmonic situation. (Chatter essentially, even if it doesn't actually chatter).
If that were me, even though you're doing the headstock thing, I'd probably drill a center and support the end, just long enough to see if that fixes the problem with the finish. Not to measure that specific cut, just to rule out variables.
I'd also probably play with the speed a little, as going that slow probably isn't helping. It might be a much faster speed that you need and you do have room for that as far as the materials go. (Don't push until you're worried about the part coming loose..... It sure isn't worth that....), or it might be a slight speed adjustment to get between resonant frequencies so it'll settle down a little. Generally speaking, that is pretty much an unacceptable stickout. There's always an exception to every generallization, but there's kind of a reason that it's generally frowned upon.
With that said... When I went through my lathe, grinding high speed steel was new to me, and it took me many go-rounds to get a tool ground that would cut smoothly with that kind of stickout. Can you grind a tool? Do you have alternate inserts you could try? Just to pick on one more variable?
Actually, the FIRST thing I would probably do... I'm sure you've studied up on doing the cuts/measurements that you're doing, if this is redundant I apologize, but I'd hate to see you go down a rabbit hole, when I believe you have evidence that there's a rabbit hole right there for you to fall into.
I'd attach a micrometer to the carriage/cross slide/comopound slide somewhere, somehow, doesn't matter. I'd take that indicator and watch the test bar as you move the carriage across both test cut areas. If you CUT the bar from a tool mounted on the carriage, then the indicator mounted somehow to the carriage will read the same reading across both of them, regardless of any taper induced by a misaligned spindle. If you DO get a different reading on that test, then you have some deflection in the equation that's going to have to be addressed before the diameter measurement will actually matter too much. If you've got chatter like that, ODDS ARE it came from the bar, and/or it came from somewhere else, but either way, cause or effect, the bar participated in it. That chatter will have a different degree of freedom away from the chuck than it will near the chuck.
If that indicator sweep mounted to the carriage somewhere gives a good enough result to get a needle reading you can work with... You could go ahead and use that undesirable finish as a basis for as it is for these measurements. I "suspect" that it's not as bad dimensionally as it looks by eye. If it tickles the indicator more coarsely than the accuracy you're aiming to hit, then you'll a little more obligated to sort the finish out first.