I found the answer: the SysEx message works!
On the message, nn = the device ID, c = the MIDI channel, b = the bank number.
The MIDI channel settings are 00 to 15 for channels 1 to 16.
The base channel of the H3500 was set to 4. By setting up the channel on the message (c) to 3, it worked.
It is not necessary to turn the Sequencer function On for it to work.
A second message in Program Change (MIDI channel, PC #) has to be entered as well. Once these two messages are programmed on the MIDI controller, the H3500 will switch presets in between banks with no problems.
Hope this helps other users!