I did a search for "transformers" in this group and found next-to-nothing, which I thought was odd (after doing a bit of research). It seems like the output transformer is one of the most important factors in what sort of sound is possible from an amp. (But I'm a newbie and just beginning to investigate the topic, so I'm all ears for correction.)

Here is what one page said:"The output transformer in a push-pull guitar amplifier is the last stage of the audio path before getting to a speaker—it’s one of the large blocks of metal mounted to the amp chassis (or speaker, as is sometimes seen in older amps). The transformer’s function is to convert the high-voltage/low-current signal from the amplifier’s power tubes into a low-voltage/high-current signal to power the speakers at a low impedance. It is responsible for how efficiently the audio power of an amp will transfer to the load of the speakers, and it prevents hundreds of volts (DC) from passing to the speakers."

I intend to investigate more, but I thought I would throw out the breadcrumbs to the info and the pieces of the puzzle that have gotten me interested in the transformer component in amp building:

I started by searching for "DIY Pignose amp" and found this discussion about the "secret" of the Pignose. That took me to an investigation of exactly what a push-pull transformer is. I then focused it a bit more by adding the words "guitar amp" to the search.

Switchable Single-Ended, Push-Pull Guitar Amp:

http://www.ampbooks.com/home/amp-technology/amp-patent-7173488/

This looks like a very cool site with lots of info. Check out the tutorials & technology links at the very top of the site.

If you look at some of the descriptions for various replacement transformers you will find other pieces of interesting information. Like on this page, one transformer's description says: "Will produce harmonic colouration on overload" and you can also find what output transformers are used in different amps by seeing things such as "Suitable for VOX AC50 4 Mk2", etc.

Finally, you've probably already discovered the excellent site "Instructables". There are some interesting tube amp builds on there, like this one and this one, which include info on the push-pull transformer's role in the amp. (There are probably more, but just thought I'd share two.)

Most of these references are to tube amps, so I'm not sure how much the role changes in solid state designs. 

Anyway, I hope these links are helpful to someone and that this thread might serve as a jumping off point for discussions related to output transformers in amp builds. Thanks for reading!