Good call. In that situation I would probably come into Kyobashi by the Keihan line, which is the most interesting line to ride between Kyoto and Osaka as you go through people's backyards at high speed. If you have a lot of stuff, and haven't shipped it ahead to KIX, you can lock it up there. Then see Osaka Castle. If you have time in the afternoon, head to the Umeda downtown area. Get dinner around the Dotonbori canal in Namba and enjoy the lights. Then either take the Nankai train to the airport from Namba, or head back to Kyobashi to collect your stuff and catch the JR rapid service. Be sure to check the train schedules. Fortunately you can almost always make do with a tight check-in in Japan because everything is so efficient.

If you have good legs, enough time, and a sufficiently light encumbrance, you can walk a few clicks down the Midosuji avenue from Umeda to Namba, which gives you a good taste of downtown Osaka and also lets you visit the Mido temples for which Midosuji is named.