I believe what you are hearing is the newly added Fulltone Super Trem pedal that Joe uses currently in his rig. I like leslie/chorus/tremolo pedals for the slow sad thing. Tea For One is more of the leslie/chorus thing, IMO I'm hearing a tremolo in The Great Flood and John Henry.
'67 and '74 Fender Twin Reverbs, '74 Marshall 1987 lead mkII, Metro Superlead 100. Pedals from TC Electronic, Ibanez, Dunlop, BK Butler, Electro-Harmonix, Fulltone, Maestro/Gibson, Loopmaster switching, VoodooLab, Boss. Gibson and Fender guitars, Dimarzio pickups.