Is there any way to output analog signals with greater resolution than 8 bits without adding more hardware?
Bottom line is without hardware not really, sorry.
Using the internal analogWrite only gives me 256 different values,
That only gives you a PWM signal not an analogue one. You will have to filter this, however to get it smooth it needs to be filtered so much that you won't be able to change the output fast enough for your laser effects. This is because all the changing is absorbed in the filtering.
Now I wait for software schemas to come flooding in from people who won't have to implement it, because yes you can do many things with software that are simply not worth doing and in my opinion this is one of them.