Try highway buses such as Willer Express:
Cheapest is still the bus though.
Taking Kintetsu from Nagoya to Namba takes almost 2.5 hours. Taking Shinkansen from Nagoya to Shin-Osaka takes 54 minutes. Add another 20 minutes or so if the final destination is Namba (via Midosuji subway line) so allow 80 minutes total. Kintetsu is of course more economical.
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