The shape of your vase in french is called coloquinte, perhaps you come across some examples I haven't spotted yet.
I haven't had the time to find out if Muller did commissions for other brands, but as Etling wasn't a producer but 'éditeur', wholesaler/dealer of fine arts and a designer, it could be a possibility. Dealers in fine arts were pretty common in France at the time, creating their own brands but commissioned and produced by other well known companies. Maybe it is a sample and the order never went through?
Sandblasting was done a lot by Scailmont and a few other Belgian companies and just a couple in France. It is indeed not a common technique and I don't know why. Perhaps it was less popular or too expensive … or just messy
Daum did a bit, Jean Luce, Legras and a couple more but i got the impression always on a small scale.
Re mould sharing, I've mentioned this before in another thread that in the 20ies and 30ies before copyright, copies were not uncommon. Marius Sabino was quoted in a report complaining about the 'copieurs d'étalages', specially hired people who were literally standing in front of a shop window display, sketching the designs in a notebook, to be used elsewhere but I'm not saying your vase is a copy in shape or design. I always find it difficult to believe that moulds were shared by different companies because they were so expensive to produce, but saying that, i have never looked into that to be honest.