I can't cut a straight thread, on my lathe
The only thing that makes since to me is that you have to much stick out from the chuck and are getting a lot of tool push off. What size material are you threading, what material is it, what type threading tool are you using? If it is something that has to stick out beyond a 4 to 1 ratio then support it with a center in the tailstock.
sounds like the compound is loose and being pushed off the work.. Heres a test .. Do a radial thread , with the compound parallel to the work .. So stop the modified flank cutting ( 29 degrees) and just go straight.. lock the compound because its now eliminated from the process. Lower the tool height just below perfect , and I mean by .010 or so , nothing dramatic..keep in mind infeed will now be adjusted at the crosslide in this configuration
Are you using the tailstock to hold you work in center? It could be the the tailstock is not centered. There are aluminum bars that are certified for checking tail stock center for under $100.00 and they are worth every penny, and will save you a lot of headaches down the the road. A tapered thread or any type of taper cut usually means tailstock is out of alignment, that would be the first place I would look. You can try this https://www.amazon.com/BLAKE-Blake-Co-ax-Indicator-Set/dp/B005PX7QV8/ref=sr_1_2?ie=UTF8&qid=1518316761&sr=8-2&keywords=coaxial+center+finder or you can try this http://www.penntoolco.com/27-000/?_vsrefdom=adwords&gclid=EAIaIQobChMItNXdj-uc2QIVgx2BCh1jkwDREAQYASABEgLWAPD_BwE. The second is a cheaper option the the blake co-axial but I don't know how much machine you want to really d=get into. I would get one from penntoolco personally. You can look for others out there just make sure they are certified.
Does your lathe cut a taper when you just take metal off bar stock, no more then a inch or two? Are you cutting between 3 jaw and live center in the tail stock? are you cutting between centers? Important did you indicate anything in before you started your threading, or just skipped the most important part of the threading job? This is what kills most operations on the lathe is the lack of setup. 30 minute set up to do a 15 minute job equals 1 hour shop rate or can make 2 for roughly same price :), all ready set up. Training goes a long way here when it comes to threading. Are you using hand ground tool steel or carbide and who ground the tool blank? Type (name) of lathe would be helpful to.