Do you know where the MT3 ER32 collet holder came from? Is it an Asian import, or of European or US manufacture? I have an Asian MT3-ER32 collet holder, and best I get from it is about .001 inch. That is better than I got with the Asian chuck that came on my Asian HF 7x10 lathe. IIRC, I get about the same runout in the Atlas TH42. My set was about $60, so I wasn't expecting a lot. The chuck was actually good, relatively speaking, with about .003 inch runout. For a 3-jaw chuck that isn't bad. For the Asian lathe, I bought and used a 13/16 inch reamer, and reamed out the nominal 19mm or 3/4 inch spindle through hole. The small end of a MT3 taper, according to the chart I just looked at is .78", just a bit over 3/4 inch. Yours is unlikely to be touching the back of the socket. The taper length is 3.88 inch, from the gage line to the end of the tool is 3.69 inch, and the depth of the socket hole is only supposed to be 3.31 inch drilled, and 3.25 inch reamed. Most of the data above is from page 910 in the 26th Edition Machinery's Handbook. If you can, measure how deep the MT socket is, and how deep you? have to go to get to the rough part. It may not be your spindle, in which case reaming it won't help a bit, and may make it worse if the MT3 shank then goes in far enough to touch that roughness.
HTH!
Bill in OKC
Bill in OKC too