Sometimes just a wee bit of oil on the screw threads can make all the difference between stupid hard to turn knobs, and ones that behave like they should.
That part is called a headpiece. It's not plastic but rather made from an alloy metal. Try headlessusa for a replacement. Another alternative would be to keep this headpiece but use a string adapter... although that would require single-ball strings.
This is the Steinberger forum which is all about headless guitars and basses. I believe you wanted to post this in the "Stanton" forum, with "Legacy Products" sub forum.
Don't know if this will help but here's a link to the parts page for your instrument.
http://www.steinberger.com/Synapse-Accessory-and-Part-Information.html
I sell single ball string adapters on ebay under the seller id pwefx21tw. Available in either brass or aluminum for 4 & 5 string bass and 6 string guitar. If you're still in the market for a string adapter, my string adapters work perfectly.