I just came back a week ago from staying at the Hilton Tianhe, a wee bit north of the Park Hyatt. Took the old Intercity Through Train from Hung Hom into Guangzhou East Station, and the new high speed rail out of Guangzhou South Station back to Hong Kong.
Although I enjoyed the novelty of the new high speed train, and going through Chinese immigration/customs in Hong Kong at the new station, to be honest getting to Guangzhou South station from that side of Guangzhou was kind of a pain. I was planning on taking the metro, but I had a carry on and a full suitcase, and my train was departing at 8:20 pm, so I didn't want to mess around with the evening rush hour, so I took a taxi.
Even though the train from Hung Hom is slower, I think the total travel time to your hotel would be about the same as the HSR, considering how close Guangzhou East is to the Park Hyatt. It's 3 subway stops south (same line, but with a change at Tiyu Xilu station) or a quick taxi ride.