On my still new LMS 7500 (not your 7" but 8.5" and from the same platform) I'm getting a taper of approx .001" per inch of turned length, most at the first and last inches. However, the wobbling of the tailstock when it's moved along z closer to or away from the headstock could well be, and probably is, the cause; I need to take the time to figure out how to improve this, in the lathe or my operation of it. If it turns out that i need to consider the first and last inch as waste, that might not be the worst of all results.
My turning is mostly in delrin, using CCMT or a handmade HSS tool, running around 600 rpm. I use CCMT because it works so well on delrin, with 20-50 thou cuts. I use the HSS tool for fine cuts and finish.
Tim