I know the intro to the studio version of white room is overdubbed, but have you come across a combo of effects that would give the intro Gm-F, Dm-C part as single line harmony with swell and delayed notes? It sounds like some of the sounds swell after the initial beat. Anyone know of a programmable device that could be set to really nail this? Orville Maybe? Older Eventide unit?
Actually, I think it's a combination of individual fuzz guitar notes mixed with cello. The staggered attacks comes from the fact that all the individual notes are overdubbed, and intentionally hitting the downbeat in two places. I don't think you can duplicate that with an ordinary guitar. Cream never did live. You might get close with a guitar that has a hexaphonic pickup, like a guitar synth, or a Roland VG-88 set for hexaphonic fuzz.
Maybe you could try a single delay (around 250 ms or so) with the mix set more toward the delay so the second hit is louder. Then add vibrato with an expression pedal, a lot of multifx units can do that. Run all that into a lot of reverb, and that's about as close as it gets without the hexaphonic thing going.