There are three choices if you really want to experience the high speed:

Take the high speed train from Guangzhou to Wuhan (about 4 hours), then Wuhan to Shanghai (about 5.5 hours). Although it is a detour, it takes less time than a normal train from Guangzhou directly to Shanghai, but costs more.

Take the high speed train for a short distance and get off at one of the stations, i.e. Chenzhou, Shaoguan, Zhuzhou...and then change to a normal train to Shanghai/Hangzhou. It saves money but takes more time. Please make sure there are direct trains to shanghai/hangzhou from the stations you may get off. Also, the train may depart from a railway station different from the one you get off.

Take the high speed train from Guangzhou to Wuhan, then change to a normal train to Shanghai/Hangzhou.

Not sure if you'll travel between Shanghai and Hangzhou. There are high speed trains between them.