Here's what I think you're after.
This is a 2x8 matrix of LED strips. Expand as needed.
The top transistors can be driven with UDN2981, which is comparable to ULN2803, but has a higher voltage drop than just a single transistor if I recall the data sheet correctly.
Multiplex by driving the anodes, drive one cathode.
Drive the anodes, drive the next cathode.
etc.
Expand upwards to make 8x8 matrix.
uln2803a.pdf (431 KB)