Thanks for the replies. Yes, one cup at a time is what I did. The lower (alloy) cup went in just fine. Couldn't get the upper (steel) race to go in straight. As I said, this is two misses in the last two tries. I think that means it's time for the proper tool. I don't mind taking things to my LBS when needed, but I also like doing things myself (even if I sometimes mess up).

In the end I bought the Cyclus tool from Slane Cycles, a new-to-me UK vendor. The price of the product was good, as was the shipping.