Thanks a lot to everyone for your very helpful replies.
I should say at the outset that the re-tramming was unavoidable after I had tilted the head to gain access to the stripped high-low gear so that I could replace it. A separate thread discusses this. I intend to post an update there when I have time. Use of a tilting vice removes the need for me to tilt the head at other times, or at least has done so far.
It was the first time I’d had to re-tram the mill; from the factory it was trammed to within a thou over a sweep of 14 inches. I’ve improved on that a little now with 0.01mm over the same distance.
Several of you (Clive F., S.O.D., DC31k, John MC, Noel, Tony, Dave W.) have drawn attention to the design and/or finish of the machine being likely to be behind the present problem. Clive’s recommendation to pull the head off and give things a thorough looking over is something I definitely intend to do at some point, but since I’ve only just had the chance to get my mill working again after six months of it being out of action, I’m loath to prioritise the time for head removal and re-engineering just at the moment.
As Dave S.O.D. suggests, a downside to this type of mill is the head-locking mechanism it happens to have. Others (e.g. YouTuber Olly of Olly’s Workshop in his side-by-side comparison of a Sieg SX3 and an Amadeal mill much like mine) have pointed out that the two locking bolts on my type of mill (one vertically placed over the other and them being rather close together) probably does not make for as secure a head locking system as the one-bolt-either-side locking system found on, for example, Robin’s mill and John MC’s and the Sieg SX3. I’ll try to photograph mine up inside the head later so people unfamiliar with my typeof mill can see what we’re dealing with.
My main takeaway from this experience, besides the excessive labour involved in tramming the mill and the feeling that my mill is almost certainly “not quite right in the head”, is the concern that, if locking down the head causes this much movement so easily, in use the head may be inclined to move out of tram far more easily than is desirable. I’ll certainly be checking the tram again very soon to see whether things have moved. There was no indication it had moved away from the factory setting before I tilted the head, though I’d not checked the tram for about six months previously.
I’m aware there’s a lot more content in people’s replies to respond to than I’ve responded to in this post, for which I apologize, but I do aim to come back to the thread later when I have more time.