It's definitely the 35W4 (B-) that is the source of AC ripple. It's a single diode, whereas the 25L6 (B+) is a dual diode and does a better job in smoothing out the DC.
I'm measuring 2.4VAC at the 35W4's plate and it gets dropped to 1.6v at the junction of the 10Ω and 270Ω - only .2VAC is leaving the smoothed DC coming from the 25L6.
I'm wondering if I should try putting a 47uF or something between the plate of the 35W4 and the 10Ω?