The 650's work pretty well with the Quickie when using a decent transformer. I called Edcor and ordered a set of units that another Bottlehead had specifically made for this purpose (I can't recall the part number at the moment, but a quick search of the forum should bring it up). I initially wired these in the Quickie as standard 8k:250 ohm transformers, but found that upping the parafeed capacitors a bit (to 5uF) and tying the transformer primaries and secondaries together in an autoformer arrangement made for a slightly more satisfying bass response.
It used to be that we would use cheap 70V Speco line transformers for this job, but the manufacturer changed that particular model and people have said that the new ones are not as good. I never found using the Speco to be all satisfying with headphones, anyway, as they have a rather high bass rolloff. The Edcors are about $12 each, so the cost is still very reasonable.
I rarely use the HD650's with the Quickie, despite building it for that purpose. The Crack is just so much better.