Piston type QCTPs are not rigid. I had the same problem too when parting. Went to a wedge type and the problem disappeared.
I've just parted a 1" diameter bar without jamming or throwing the belt, which it used to do regularly. With this system I can use one hand to feed the tool and the other to hold the oil can, I don't need the 3rd hand to keep the speed under control.
https://www.ebay.co.uk/itm/Universal-Quick-Change-Tool-Post-Holder-Kit-Set-for-7-x10-12-14-Lathe-Tool-Set/253043771912?_trkparms=aid=111001&algo=REC.SEED&ao=1&asc=20160908105057&meid=9849d2320f604ae8a4c813608abd69bc&pid=100675&rk=6&rkt=15&sd=232776570816&itm=253043771912&_trksid=p2481888.c100675.m4236&_trkparms=pageci:9443c793-a0d8-11e8-9d05-74dbd180dd4f|parentrq:3fa78b851650ad41723f145bfffa5323|iid:1
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The whole construction is aluminium.
Been giving it a bit of a workout today. Decided to turn a point on the end of a M10 HT bolt, had a problem with the workpiece riding over the parting tool when the diameter was down to about 2mm. I could feel movement between the tool holder and the body of the QCTP, but there's absolutely no movement if you try to force it by hand. There is also backlash in the cross slide thread which allows the tool to move forward when the tool grabs. Added to that there's slight play in the spindle. I adjusted that out but it returned.