I had similar problems with my first couple lathes (Grizzly G9972Z 11x26 and Grizzly G4003G 12x36) using both HSS and cheap import carbide. For me, switching to brand-name quality carbide inserts made a big difference. I'm using Iscar SGFH/R/L blades with GTN/GTR inserts in the 1, 2, and 3mm widths. These sizes span a cut width of 0.063" up to 0.139" depending on blade/insert; I use the 2mm most frequently. I also make sure to get the grade meant for unstable conditions and slower F&S - IC328 is the one I can recall. They will run about $5/insert on eBay but I have yet to burn one up. Any big brand is probably similar; I only started using Iscar because I received some blade holders in a cabinet I bought at auction.
Someone linked the Iscar Heligrip - that could be a good option and maybe better value since you get 2 cutting edges vs 1 with the SGFH. Somewhat limited DoC tho.
This is after all the other (good) recommendations like parting right next to the chuck, proper tool height, lock cross-slide and compound, etc... I also played with turning with the blade upside-down to aid in chip clearance (this didn't really help me at all). With SS you have to feed to get the cut. Too slow or dwell and you'll smoke the bit. All these recommendations helped, but for me a quality insert made a big improvement.
