Curious! I elected to do the manual update rather than try plugin, which has not been updated in over two years. First I went to JetPack to make sure my site had been updated recently, and it had. Then I went to Plugins page to deactivate and delete old version of GP Premium and then install the new. But lo and behold! The automatic update was now available! Somehow visiting the JetPack page seemed to cause a refresh of the plugin info, and so I did not need to do a manual update after all!
So I believe I am now set on both sites. Thank you, Tom and Leo!