Apskip, trains in Malaysia are painfully slow when compared to the European network... The only direct train I know of leaves Butterworth at 7.00am and arrives in Singapore at 9.30pm, a journey of 14h30. If leaving at night, there is the option of changing trains in KL Sentral, which would mean a journey from 8.24pm to 4.05pm the next day, a journey time of 19h41.
The 6.5h you mention should only be able to get you from either city to Kuala Lumpur... Would you mind sharing your source?
Buses are the much speedier option, with journey times approximating 8.5h. These leave frequently between 8.00am and 10.30am, then again from 8.30pm to 11.00pm.
I'd love a free for all. Release teams after the last direct flight to Singapore at 9.15pm, then let them choose whichever mode of transportation - train, bus or plane - they want; the first plane in the morning through Kuala Lumpur gets in at 7.05am and the 10.30pm bus at 7am...