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Dave, there are very great differences between an AC series connected motor and the DC motors and their controllers that must be understood before you make a choice.
The orginal selection of an AC series connected ?motor was made for several reasons (largely cost I suspect). An AC series motor has a very good (high) top speed but a terrible load regulation. In that it is very forgiving of "chuck crashes" and a such not a bad selection for a what could be considered a beginners lathe which is small enough that it is easy to get fingers mixed up in the works.
A DC motor and a proper "chopper" speed controller are the exact opposite in that what ever speed is selected the motor will try and maintain what ever the load upto the current limit of the controller. Thats very good for quality finishes and large amounts of metal removal ( compared to the AC motor anyway). And of course being able to set the speed perfectly for required cut ( and not have to keep changing belt settings). The controller reference "pot" can always be hooked up to foot pedal if required.?
For me changing to a DC drive was a "no brainer" I went to a much larger motor but only used a fixed toothed belt drive with only one high speed ratio. The result was a very wide chuck speed range without having to keep changing pulley ratios, but still acceptable maximum torque (plus a minature DC breaker to control chuck crashes).

Please excuse the "condition" of the lathe other dusty operations are ongoing.

Bob