It is true that all reactions should be cleaned up afterwards. And shit in = shit out, no matter which way you wanna reduce it. (So clean ephedrine is better, with less impurities to be reduced)
Something that I have found however, is that NONE of the articles I have read about performing birch reactions discuss over reduction, which is highly possible - considering that none of them give a method for weighing Lithium/sodium/alkali metal to the accuracy required (not easy to weigh something that is so reactive). You put in too much lithium (or whatever metal u choose), you'll end up with di-meth.
It seems to me that perhaps it would be better to add just a bit too little - end up with some unreduced ephedrine - and seperate the mix?