What is this adapter and what can I replace it with for simpler operation?
If you are capable of splicing coax and terminating the pigtails to the screw terminals reliably with heatshrink, wire and solder , then this can work for you. Or find a tech who can make them for you, or ask Digikey to make the pigtails.
  Male-Female extension cable AWG 18
https://www.digikey.com/product-detail/en/tensility-international-corp/CA-2216/CP-2216-ND/1129479
The heatshink is intended as the braid insulation-cut-edge strain-relief.
Plan B
tin-lead Solder the wire ends with only enough solder to coat all the wires and allow heat to wick it up just inside the insulation.
For frequent teardowns, the frayed wires should no more be a problem.