It is often the case that close up images of canes in Vasart / Strathearn weights [and many others, too] are difficult to achieve. A major reason is striations ("wreathing") in the glass, which cause the effect you mention when looked at in close detail. Another reason for poor viewing of canes is that small areas of air bubbles can occur over individual canes. Aslo, tiny stress cracks can occur over and around canes during the final cooling process.
Your point about putting another layer of glass over the dome is spot on. Generally, after picking up the canes on the initial gather of clear glass (or on the coloured layer) another gather of clear is added and the whole is worked into the dome shape. In some cases, two or even three layers of clear can be detected within the dome.
Sometimes, it is possible to get a reasonable photo of a cane (or a small group of canes) by moving or tilting the camera slightly and accepting that the image will not be a full "head-on" view. Another thing to try is to place the weight in water that just covers the dome and to see if this helps to bring out the cane details - occasionally it will do so.
The other weight you show is certainly either a Vasart or Strathearn. And, just like the first weight, even if it had a Pirelli label on it, it would still be Vasart or Strathearn. The Pirelli label was just an indication of where it was marketed, not where it was made.
As for digital cameras providing good close up facilty, most modern cameras in the "medium" price bracket (and always cheaper in the US than in the UK!) will now provide multi-megapixel images [of a physical screen size that Bernard once aptly described as showing up in his neighbours room]. This means that you do not really have to get too close for a good sized image of small detail. Just take a photo of, say, a quarter section of the weight and most of the canes in that image will be large enough and of good enough quality for the purpose you need.
However, when I first started cane photography, I was using a Nicon Coolpix with a "macro" focus distance of about 10 cm and "only" 3 megapixel resolution. To get better "macro" results, rather than spend £200 on a Nicon macro attachment, I bought a compbined 3x / 5x magnifyer from a stamp collecting / model making shop and placed this over the front of the lens. With the Nicon, the camera lens was inset within a screw thread, and therefore the magnifyer lense woudl not cause any damage. By trying the 3x and 5x separately and in conjunction (giving 8x), I could obtain very good close ups of most canes. And the magnifyer only cost me £5. I still use this setup today, albeit with a later 4 megapixel version of the Coolpix, when my latest 6 megapixel digital SLR with all the specialised lenses and so forth fails to give the result I want!