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@provenrad
IT depends whether you have (a) a modern cassette hub (as you say you do), where the cogs all fit on a splined body and held with a lockring OR (b) a threaded freewheel, where the freewheel mechanism and cogs are one unit that screws onto the hub. (original 1970s parts means you are (b))
If (a) - use a cog and spacers, (b) - screw-on freewheel (ACS / Shimano) will solve your problems.
http://www.sheldonbrown.com/singlespeed.html#freewheelhub