4-6 week turnaround is pretty shit. You do indeed get what you pay for.
I'm considering a different scope. Any suggestions (under £600)?
Difficult, as for that money you only get B-brands and they all have some issues. In Europe, Siglent still wants you to go through the reseller for warranty (in the US they do service now directly) and I doubt it will be anything quicker than Rigol. Plus Siglent scopes in general are even more buggy than Rigol, but I guess you know that already
Frankly, with that budget, the DS1054z probably isn't the worst choice.
I looked at the Tek TBS1052 but the spec sheet is pretty crap. It'd do fine for what I need to do however and the turnaround is fast. I'm slowly moving into the professional space again after a 15 year hiatus so I'm after something I can trust.
Yeah, Tek is pretty shit, and that's not just the antique TBS Series. They made the best analog scopes back in the day but their digital scopes have always been sub-par. Plus their support is a far cry from what it once was. I'd avoid them like the plague.
The mentioned Hameg HMO1002 might be an option. It's a much better scope than the shitty TBS.
Since your budget is limited, have you considered the 2nd hand market? A 2nd hand Keysight DSOX2000A Series scope might well be possible with your budget, and while the specs aren't best in class they are decent and the scope is pretty reliable. Plus you can buy a Keysight "repair agreement" which is pretty much a warranty and can be bought for older kit where the original warranty has run out, and it's usually quite cheap, too.