Time for an update. I communicated with Claire at Eurosport and she was very responsive when I complained about the synchros. She said that these synchros were from a different supplier in Italy than she has typically used in the past, but she has not had any complaints about them before. She had just got another batch of synchros from her usual supplier and she compared the gaps between the two batches with a used 2nd gear that she uses for reference and there was definitely a larger gap with the newer batch. She sent me two from the new batch and they were much better.
What she also did was send some nice pictures of some 2nd gear cones for me to use as reference to compare to mine. Here they are:
This is a new 2nd gear showing the sharp, unworn ridges on the cone.
This is a reconditioned one that they sell.
Here is a used one that has some flattening of the cone ridges, but still okay.
Last, there is this one that is really worn out.
Here is mine that looks a lot like the used photo from Claire.
Here is a new OEM 2nd gear that I got from Italy, thanks to a link from Doug Martin (rx1900).
I tried to source some OEM Fiat synchros, but the two I ordered from an Italian parts site, turned out to be too small, even though they claimed they were genuine Fiat parts and even had the correct part number. They are on the way back to Italy for a refund.
So I have started to put the transaxle back together, using the new gear I bought, and the new synchros from Eurosport. Here is the gap now, 2.05 mm vs. 1.25 mm with my used gear and the worn out synchros.
While I had the transaxle apart, I decided to change the main carrier bearings. I took the differential and case halves to a local AAMCO place to have the bearings and races changed as I don't have the right kind of pullers. The guy was very informative. He has an MGB, so he knows about older transmissions. He swapped out the bearings and races for me and also gave me a good tip on evaluating the synchros. He said that when you put the synchro on the cone and give it a little twist, you should be able to pick up the gear with the synchro if it is good. If the synchro is worn out, the gear will just fall off. He was right.