Sounds like a normal computer power supply would be a good start ... those can do 3.3v and 5v at about 20a each (but about 130w in total on both 3.3v and 5v so about 15a on each is reliable) + 12A at about 30-50 amps. For 50-60$ it's very hard to do better.
There are linear regulators like LT1083 and LT1084 and LT1085 that can do 7.5A and 5A and 3A respectively.
LT1083/LT1084/LT1085 datasheet :
http://cds.linear.com/docs/en/datasheet/108345fg.pdfLooking at the datasheets it seems that
minimum forward voltages are 2v and 3.5v, but you probably need to look at higher voltages:
8.1A driven continuously :
min VFmin 2 3.5 3.5 V (R G B )
typ VF
2.7 4.5 4.6 V (R G B )
max VFmax 3.5 5.6 5.7 V (R G B)
13.5A with 25% 50% 25% duty cycle
min VFmin 2.2 3.8 4.0 V (red green blue)
typ VF
3.0 5.0 5.1 V (red green blue)
max VFmax 3.8 5.9 6.0 V
LT1084 has a current limit set at about 6.5A so you could probably just pair two of them and set them to output 3.7-3.5v with a 5v input and rely on the built in current limiting
just the same you could use 3xlt1085 with its 4A internal current limit to get the 4.6-6v for green and blue from 5v or 12v (3 lt1085 to dissipate the heat easier), with 25% and 50% pwm you're basically going to run these 3 3/4 of the time.