Does anyone know roughly how long a taxi ride from Osaka JR Station to the Osaka Port International Ferry Terminal? And how much it would cost?

Honestly have no clue about taxis to there, but here's some info that might be helpful.
Access to Osaka Ferry Terminal

Calculating the taxi fare between JR Osaka Station and Cosmosquare Station by livedoor taxi fare retrieval
site, it would cost approx. 4160 - 4580 yen during day time and 4960 - 5460 yen during night time.
(13.6km)
http://map.livedoor.com/map/taxi

It isn't really all that far if they jump on the Hanshin Highway. I would say within 15 minutes or so. I think over 4000yen is too high. Maybe try 2500yen because it includes highway fee.

There's no way it's going to cost 2500 dude, I just caught a taxi from Namba to Minami-okajima (not too far from Nan-ko) and it cost us about 2500. Osaka station's heaps further, 4000 is the minimum, 5000 tops.

Osaka Station is definitely closer to Nanko because by highway is takes 15 minutes. I drive and have done that drive numerous times and know that taxis drive quicker than me. It's definitely around 2500yen.

I'll give you a bet it's at least 4000. It might even cost more than 5000, the Hanshin Expressway goes no where near Nanko, you'd still have a long way to go once you got off it. I've been asking some hard-core locals, and they all agree with me, I'm not listening to no gaijin on the topic period.

Yes and I am sure those "hard-core locals" told you that Hanshin Highway goes no where near Nanko despite the fact that Nanko has 3 exits on the Hanshin Highway with 2 exits within a 5 minute drive of ATC/WTC/Intex Osaka. The 2500yen bet stands.