Just 2 taxis, right? I'd think trying to do 3 or more can get tricky.
I'm not familiar with the super street "Y". Does it have anti-derailing or must you pre-set (pulse a solenoid?) the branch direction when entering or leaving each loop?
What exactly are these optical sensors? Can you mount them to detect direction of travel? For example, if you are shooting a beam upward to reflect off the bottom of a taxi let's say you put a reflective bottom on just the right side of the taxi. Then by placing the optics on the right side of the roadbed (relative to direction of travel) you can detect which direction the taxi is traveling on the straight. This might simplify the relay logic.
Is soldering and/or working with small electronic components (resistors, capacitors, etc.) "allowed" or to be avoided at all cost?!
In any case, I'd think you can cobble together a handful of low-cost eBay relay modules (about $1 per relay) and get something running for, say, $10-20.
Sounds like a fun project! 
