The reason the transistor can't be turned off (post #27) is that the resistor value to bias the transistor on is too low and current too high for the Opto to sink, so you need more gain to allow the use of a higher valued resistor.It would appear to me that the problem is not transistor current gain . The transistor is already turned on.
The problem is turning off the transistor.
It's actually the low gain of the Opto that necessitates a high gain transistor at the output to drive the relay.