Most convenient stay for Kansai in Osaka

Hiello.
As I will be flying home from Kansai airport this time in Japan in quite an early morning flight I need to be there around 6 in the morning.

For some reasons I wish to stay in central Osaka for the night. There are options of leaving from Shin-Osaka, Tennoji, Namba, as far as I have seen. Are there any other locations that could be equal for a early morning train? Does not have to be the JR Haruka or Rapit as I expect the first departing trains will be not too crowded...

I don't want to take a bus as I dont rely on traffic...

Since most hotels near Namba and Tennoji are quite expensive, are there any other convenient locations you can think of?

I always try to avoid kansai departures before around 10:30 as the limo buses leave Osaka and kobe around 8 in order to make these flights. You might look into the hotels (two I think) that are right on the airport. Would avoid that terrible early morning rise and stressful trip to the airport. Hope this is helpful,

First train from Namba to KIX using Nankai arrives at 0558.

First train from Tennoji to KIX using JR arrives at 0609.

You dont have many options since your flight is so early.

What time is your flight home? Because being around 6 am at the airport means you either have to sleep in hotel in KIX or sleep inside there.

Sleeping in KIX http://jpninfo.com/44482, http://www.sleepinginairports.net/asia/osaka.htm.