Yep, the transformer numbers definitely make a difference. Using my no-load voltage (6.64V) and the spec'd power rating gives me 97mΩ, which in turn yields 3.4A stock and 3.7A w/CRC.
The remaining difference is probably down to the rectifiers we're using in the model. Your 1N5828s have a lower voltage drop than the MBR745s used in the kit.
Here's a reasonably accurate model of the MBR745s if you want to dump it in your PSUD2 rectifiers.txt file:
MBR745, SS, 0.007, 9, 4000, 45, 150, 7.5
In any case, sounds like I need to keep an eye on transformer temps. I assume it will get externally warm to the touch before it overheats?