Airport to New Otani Osaka

I am given the following options for transfer from Airport to New Otani Osaka. Which way will be more convenient? We are in a group of 8 adults + 1 infant (19mth old) :

1) To take trains, please take JR-train to JR "Tennoji" station and change the
train to JR-LOOP line. Our nearest station is "Osaka Jo Koen". From the
station, it is about 3-5 minutes by foot. If you have large luggage, it
might be convenient for you to take a taxi from Tennoji station to our
hotel. If you take a taxi from Tennoji station, it takes 10 to 20 minutes
and costs around JPY 2000

2) Take the bus to UEHONMACHI and take a
taxi from the bus terminal. There are 2 or 3 buses every hour and takes 50
to 60 minutes to Uehonmachi and costs JPY 1300 per person. It takes about
15-20 minutes to our hotel from Uehonmachi by taxi and costs around JPY1000

3) Take Limited Express Haruka or JR Kanku Rapid to JR Loop Line Tennogi
Station and CHANGE to another line to reach JR Osaka-Jo Koen Station

see this timetable first.
http://www.kansai-airport.or.jp/en/access/train/jr_time.html

''OT'' service brings you to Osaka-jo Koen station without change.

''KB'' service directly takes you to Kyobashi station(one stop north of Osaka-jo Koen). from there you can take a taxi or train to Osaka-jo Koen station or whatever.

Your hotel and JR Kyobashi and Osaka-jo Koen stations
http://www.newotani.co.jp/osaka/img/access_map.gif

My present for you, see the page 5. :)
http://www.jnto.go.jp/eng/location/rtg/pdf/pg-505.pdf

Thanks Ts! I will be reaching sunday morn 7.30am, hence OT service will not be available.

Is there any difference taking ''KB'' service directly takes you to Kyobashi station(one stop north of Osaka-jo Koen). from there you can take a taxi or train to Osaka-jo Koen station or whatever VS taking please take JR-train to JR "Tennoji" station and change the "Osaka Jo Koen" or taxi?

Also, how long does it take to from New Otani to walk to Osaka Castle? Is 2hrs sufficient for the castle?

Thanks!

Fare : no difference
transfer : no transfer needed to Kyobashi Station from KIX.

New Otani Website says 8 min walk takes you from Kyobashi station to the hotel. and the above-the-ground pedestrian walkway is equipped.

I'd personally choose this "not-the-fastest" but "the easiest" way if I were a traveller with a luggage. You can also take a taxi from Kyobashi to the hotel.

2 hours at Osaka Castle are adequate.