> not sure why the oscillator loop has an extra c/r in the network. it must not shift the full 60 degrees in each c/r section maybe?
You need 180 degree shift. If there is enough gain, this will happen.
Two R-C can not-quite reach 180 deg. Even a gain of infinity won't oscillate.
Three R-C can approach 270 deg, and will pass 180 deg with a loss about 27. Amplifier gain over 27 will oscillate.
Four R-C can approach 360 deg and will pass 180 deg at quite low loss, maybe 4? So you don't need much of an amplifier to make it ring.
The flip-side is the extra R-C parts.
BUT -- AND -- if you want to VARY the frequency (tremolo rate) with a single pot --- one variable resistor in a 3 RC network gives very small change, one variable resistor in a 4 RC network gives even less range. As it works out, trem usually does not need a huge range. If one of three Rs change 10:1 (200K to 2Meg) we get 2:1 range, which apparently means we can "match tempo" with the musical beat (or a 2:1 ratio faster or slower). We can often get a 20:1 resistor range and 2.8:1 speed change. One variable resistor in the 4-RC network only gives 1.77:1 to 2.1:1 rate range.
And back off. This is an ORGAN trem. Organists often live with no Depth or Rate control. (The original mechanical shutters in front of a box of pipes could not manage this complexity.) You are an electric guitarist. IMHO you want a guitar-adapted tremolo plan with wide range of depth and rate to match your wild-to-mild musical stylings.