Bought a SmallRig cage for my A7iii having used them on both of my A6000 and liked the quality and value. Never had an issue using my Sony lens adapters on the A6000 in the cage, both the LA-EA1 and LA-EA2 worked perfectly. Use the LA-EA1 with my Tokina 11-16 on the A7iii but take off the 1/20 mount on it. After a almost a two month wait for my LA-EA3 to use with my Sigma 70-200 it came in today. You can't use it with the SmallRig cage. The mount is built into the adapter like the LA-EA2 & 4 . Never tried to use the LA-EA2 on the cage and just assumed the LA-EA3 would work. NOT.
So stay away from the SmallRig cage if you are going the same route as me. I will send the customary email but don't expect them to do anything. I will also be trying other cages before buying.
Just thought folks should know.

I will send the customary email but don't expect them to do anything

Does smallrig say anything about supporting the LA-EA3 on their website?

SmallRig has not replied yet. I did however contact Tilta after seeing their new cage on Newsshooter.com and they replied that at this point they had not tested it with Sony or other adaptors.
I looked at the Shape cage it seem pretty clear that it will support adapters and I will try to find out from them if they or one of their retailers have one I can try since they are a Montréal based company.
This being said it seem incumbent to me that if you are building a cage for a camera its purpose is not to limit but to add to the kit. Especially when it is a cage for a Sony camera and designed to work on the A7iii and A9.
Just saying.....

It most likely is an oversight from Smallrig, I know they do make design changes based on user feedback and when they find out that the LA-EA3 won't fit there is a possibility they"ll add a second model to their line up, they allready did something similar with a cage for my GH5 which also has a second model that allows better access to the buttons on top. As it currently stands they only promise that the a7III fits so it's not a design fault but only something they didn't consider.

Well I hear from SmallRig and they said in so many words. "tough" They gave me what amounts to be a BS answer:
Hi friend,
Thx for your message and sorry for the late reply.
We are so sorry for this issue firstly.
But we have to say all our cages with anti-twist design are not compatible with big metabones adapter, such as the LA-EA2 and LA-EA3 adapter etc..
At present, our cages with anti-twist design are mainly compatible with E adapter and we won't consider the A adapter compatibility in the near future.

Since when does metabones make the LA-EA2 and LA-EA3 adaptor? Just someone who is talking through his butt since E mount adaptors and A mount adaptors are pretty well the same size.
As for the anti-twist well that is bull too since my camera twists in their cage unless you use a twelve inch pipe wrench on the quarter twenty screw. No rubber or cork or anything to prevent twisting in the cage at all.
In short they screwed up and didn't test any adaptors. Will be posting the cage for sale soon and will never buy from them again. Contacted Shape and I will try one of theirs next week. Zacuto has yet to reply but I suspect it won't be a problem.