With a ring inside the crystal this is an armed tension type. The Sternnkreuz 'G22' catalogue covers these which you can download at http://www.sternkreuz.de/accordion/assets/Sternkreuz_Gesamtkatalog G22.pdf
Whilst for the Sternkreuz 'ST'' range Roamer does have some specific citations (p25), for the 'ATC' range you need none are mentioned. Almost certainly therefore you'll be fine with a standard ATC crystal that meets your measurements.
The usual advice is to go 0.1 larger than the outside diameter measurement you've taken. This means when you release the crystal, after it has been gently 'squeezed' in the claw removal/fitting tool, it makes a nice tight fit.
Since you're using Cousins your best bet is going to therefore be https://www.cousinsuk.com/product/standard-chrome-ringed-glass-atc# and the 30.7mm size.
Is not that difficult really. As Matabog noted, dies threaded M6 are standard. The nice expensive set have their Dia. specified, the Chinese write Rolex just to indicate quality, but we know that true Rolex-specific dies are for the screw-on case-backs ...that's another story.
Then on AliX search "watchmaker dies", 20 pieces nylon are like$8, aluminium quite a bit more. I personally choose based on shipping times, things have improved but China post is still very slow, HK, NL post are OK, 7-10 days.
Thanks! I knew it was a "stupid" question, but I've had too many tool disappointments during the past two years (that I've been doing this) that I no longer dare to take anything for granted.
Yes, that other tool looks like a very good option, but then I would have to order dies separately. I don't really mind that, but I have much too little experience to know what to get. The ones you listed look nice, but then I can't determine if that's what I need, how I can tell if they will fit without some modification or extras, if it's just for Rolex watches, or if... and so on... You get the picture
Anyway, if you guys can provide me with a link to a nice set of dies that will fit without modifications to the tool or the dies that will cover most common needs I'll order it without a moment's hesitation
Of course it doesn't, otherwise I could not have said that it works.
However I recommend that you consider the other one posted above, which is more sophisticated and not so unnecessarily heavy. That original MKS is after all a something dating back to the 60's easily.