I am not surprised that
The Royal Mint was not able to help you, despite the fact that was through them, that the original plastic capsule originated.
To provide good protection for an 89 mm diameter coin is a unusual and tough problem to solve.
You may end up having to custom make your own protection for such a large coin, and what you end up with may be a far less elegant solution, but at least it is some sort of protection.
If I had an 89 mm diameter coin that needed protection and effective storage I would be forced to provide
my own custom protection for it:
Obtain two large clear sheets of hard polyvinyl acetate recovered from toy, tool or food packaging. Cut these into two 150mm squares, and staple the coin in between. You may find it convenient to seal the edge with adhesive tape. Build up two cardboard squares with a 120 mm hole and put these on either side to make up to the thickness of the coin.
A bit like making your own very large cardboard flip.
The cardboard should really be acid free, to slow down the rate of development of a patina on the coin.
Put into the smallest clip lock plastic bag that is appropriate.
Some bullion collectors, who have had the misfortune to have broken the original protective capsule on a large coin, may have found a better way of solving this problem, than in the way I have suggested.