What is that silver coil connecting the tubes and the anode blocking cap? It looks like an R-L VHF parasitic suppressor without the resistors.

It's not a parasitic suppressor. As I mentioned in the design section on stability, these tubes are very stable so a parasitic suppressor is not necessary as long as the grids are well grounded and there is decent isolation between the input and output of the amp.

The purpose of the 300nH inductor is to help lower the Q of the output network on the high bands and make the amp easier, or possible, to tune on 10m. I needed it because of the relatively high minimum capacitance of the anode circuitry (Ctubes + Ctune min + Cstrays). You can think of the coil as canceling part of the capacitance, or as the inductor of an intermediate pi network between the tubes and the tune cap. Doing the anode to output impedance transformation in two steps (two pi nets) like this can lower the voltages and currents circulating in the tank, although in this case the reduction is only about 15%. On the low bands the coil has very little effect.