I suppose by using tha 16 ohm tap I'll get a little more NFB.
Under normal circumstances (feedback from speaker to phase inverter, or stage before), then you're right.
Given a typical EL84 amp, your bias (voltage across the cathode resistor) can't be but 8-12v. Your amp's output power is ~4-5w. Pretend the speaker is a resistor. 5w*16 ohms = 80. SqRt 80 = 8.94v on the 16 ohm tap, at full power output. On the 8 ohm tap, it's only 6.32v.
To get your amp to make full output power, you need an voltage applied to the grid approaching the value of the bias (say, 9v). The output tube has, when this voltage is applied, a bigger voltage and current swing, as measured at the plate. The OT matches the tube plate to the speaker load, but does this by stepping down the voltage swing, and stepping up the current. We've already calculated how much a.c. voltage needs to be applied to a 16 and 8 ohm resistor to obtain the full output power of your amp.
If you think in terms of voltage only, from the EL84 grid to the speaker, 8-12vac (whatever matches your EL84 bias) has to be applied to arrive at 8.94vac (5w, 16 ohms) or 6.32v (5w, 8 ohms). If we were calculating gain, this is either almost no voltage gain, or an attenuation.
A feedback loop only works if there is excess gain to throw away. For example, say you had a gain of 40 (8v in, 320v out), and you wanted to use feedback and could accept a closed-loop gain of 20 (8v in, 160v out). The gain thrown away in the feedback is actually being used to reduce distortion or (if derived and applied the right way) to control speaker flap, reduce output impedance, increase input impedance, etc.
Since there is no-gain or even a loss from EL84 cathode to speaker, and since you will need a voltage divider to isolate the tube cathode from the speaker, you will get no useful feedback. For this injection point only, it's not enough (16 ohm tap) or really not enough (8 ohm tap). The same problem exists at the cathode follower output (voltage loss from this point to speaker, due to tone circuit then OT) and the cathode follower input (voltage loss due to cathode follower, tone circuit and OT).
Just trying to help you see what you might have already realized: that you have to have excess gain available to "throw away" in a feedback loop, in order for the NFB to actually do any work. The same probelm potentially arises when there's marginal gain thrown away in a loop, and we overdrive the input to the loop... eventually the input signal overpowers the amount of feedback available, and the feedback abruptly stops working.