I think I have found a good place to relocate the 600W transformer so
that it will be on the same side of the driveway as where this
junction is. My plan now is to run two 8 guage wires from the
relocated 600W transformer to this junction. Then let the existing
buried 12 gauge wires run from there to each spot. It will be hard for
me to change out the 12 gauge wires after the junction, since they
cross walkways and etc. But from the transformer to this junction, I
have a clear path... which is great news!
Bad news. If you merely shorten the distance from the transformer to the
junction, without changing the wiring after the junctions, this would
brighten all the lamps, so the downstream lamps will still be dimmer than
the closer one. Nevertheless, it is a safety improvement to change out the
overloaded 12 gauge wires. Perhaps your contractor would do this for free if
you could convince him the wires are overloaded. Is he even a licensed
electrician?
By the way, I used my voltage meter to measure the voltage drop across
the 2 wires coming out from the transformer. I had expected to see 12V
across them, but I dont detect a voltage drop. But somehow it
works... 
You wouldn't happened to be using a DC meter to measure AC voltage?
"voltage drop" means a voltage on the same wire at the two ends, not the
output of a transformer. The output of the transformer should be 12V, and
the voltage drop on the wire from the transformer to the junction would
probably be less than 1V on each leg.
The two 8 gauge wires will each handle 1/2 the yard. The total length
of each leg is about 40' from transformer to the junction (8 gauge),
and then another 40' from junction to each spot (12 gauge). Most of
the light fixtures are after the junction.
So some of the light fixtures are before the junction?? By definition there
has to be a junction for the light to connect to.
How do you measure the voltage at each spot of the run if I cannot
even detect a voltage drop across the 2 wires at the transformer?
Thanks for any tips....
Home depot may have free classes in electrical wiring. You can then show the
instructor your wiring plan and get his blessing.