Of course it ain't trivial, if it was everyone would be doing it... Especially as hobbyist it's fairly difficult, they spent years working on some of these things with entire teams. For example that design you linked is fine, but if you actually try to implement it you'll see there's a lot more to getting the actual performance out of it. (I tried it myself actually.) Plus just copying someone else's circuit is boring if you're not being paid for it!
But indeed, the entire point of the analog design is getting the noise floor low enough and keeping everything stable, precision components aren't strictly required actually! The clearest example of this can be found in some of the older Keithley circuits, fairly common average components which are easy to source, but they were selected for characteristics that weren't necessarily listed on the datasheet. Additionally the 3458 in some ways is actually a clumsy design if you think about it, the converter ain't that intelligent, they went for specially binned components, ...
But why do people keep thinking they need the LTZ1000 for this? It's an overkill reference for many applications, especially for 6.5 and 7.5 digit meters. It increases your BOM cost while you won't really have any significant gain from it in most cases, since I seriously doubt I'd be able to design something that can do actual 8.5 digit conversions reliably on my own. And most people who think they can do it are probably over-confident (no offence intended to Mickle T. - his design might be able to do it).
@Kleinstein:
Thanks, I was quite proud when it worked! I wonder how those daft bastards at Keysight got it working with a C0G cap though. But the main performance increase actually came from improving the comparator, its what made the multi-slope conversion feasible.