I leave a Hardinge HLV at work to a 9X20 at home so I know the feeling well.Hi MCRIPPer
Wizard69 has covered the alternatives very well for modifications or additions.
I can understand that that you are somewhat frustrated with moving from a large and powerful lathe to a small benchtop lathe having done the same excercise.
Poly Vee belts are excellent for these types of machine tools. With all low speed belt installations you need to make sure you don't exceed the belts ability to transmit the torque."Poly Vee Belts" and pulleys are easy to fabricate and fit and fairly compact.
Gear it down if you need more torque at low speed use stepped "Poly Vee Pulleys" to give a selection of ratios.
Eric
I'd shoot for a ten to one reduction. If that doesn't stabilize low speed cutting a more detailed review of what is happening is needed.