Hi Simon,
Thnaks for getting back to me about this. Since you are looking to offer 13 different colour options for each variant and there is an eBay imposed maximum of 120 variations per multi variation listing, I'm afraid you would not be able to accomplish this with a multi variation listing after all.
In light of this new information, I believe the best way to go about creating a listing for this product would be to create a fixed price item and select "Lots" in the area just under where you enter the price. Once you select "Lots", you will be presented with a field where you can enter that there will be 60 items per lot.
Of course, if you go about the listing in this manner, I recommend making it very clear in your description and checkout instructions that all buyers need to let you know which colour they would like each package of 20 in the lot to be so you don't have to contact them after the sale to get that information.
-Mike