adding an output transformer stage to a Son of Screamer type circuit

[amptramp]

If I understand correctly, then, the 100uF cap in PRR's image would lead the transformer to operate without the DC current, and thus it would not generate the even-order harmonics that would lead to a pleasing type of harmonic saturation.  Do I have that right?

All transformers introduce distortion, of various flavours, whether there is DC or not. Some more than others, of course, so it depends what transformer you use. A cheap little transformer is likely to add plenty of flavour even without saturation.

If so...would it be more advisable, then, the remove that cap, have the signal go right to R14, and put the output cap between transformer and the volume pot?  Would that create a scenario where the transformer generates even-order harmonics?

That would saturate the transformer so hard you would get no output. The best option is to build the circuit as PRR/me have already shown. Then listen.
Then add a resistor in *parallel* with the cap. This will allow some DC to leak past the cap and through the transformer primary, which will push it towards saturation. You can play with the parallel resistor value as much as you like, heck make it a 100k variable resistor and call it a saturation knob if you like.

That variable resistor as a saturation control is very interesting.  I will give it a shot on the breadboard when I try to build this thing up next week.  Question...would the resistance from the variable resistor obviate the need for R14, or would it be advisable to have R14 at a nominal value so that if the variable resistance was completely removed, there would still be a safety net of sorts before the transformer stage?

What sort of a safety net are you looking for?  Op amps are generally current limited so you may get some odd op amp saturation from current limiting but most op amps can operate into a short and if you are using a 5532, it can drive a 600 ohm line transformer by itself.  If you are using an op amp with less drive than the transformer can absorb or at low frequencies where you are more likely to run into current limiting, it may be wise to include it so you don't have a situation of a misadjusted control causing you to go into a weird distortion mode or go mainly silent because the op amp is current limiting.  In a stage situation, you don't want to be able to inadvertently adjust the signal chain into silence.

[PRR]

So don't do that to me.

I was not being personal. (Or thoughtful.) I am annoyed at the entire "internet".

I now see that my words sound offensive. I am deeply sorry.

[merlinb]

would it be advisable to have R14 at a nominal value so that if the variable resistance was completely removed, there would still be a safety net of sorts before the transformer stage?

R14 is still required; it helps to isolate the opamp from the highly reactive load of the transformer + unknown guitar cables. Without it, there may be situations where you get oscillation. Any value between about 100R to 1k should be OK though.