If you pull for 10 minutes and imediately put more in and pull 10 more in, that is the same as doing a 20 minute session.
That is exactly what I do, for a couple reasons. First being when I first started pulling I got sick and would gag it out and have to spit it out but I wanted to do a full 20 min cycle so would quickly put more in. Then after I got that under control using peppermint, I continued to spit after first 10 min and get more for the same reason you suggested... I decided it was so toxic, by the foamy texture, etc. that I figured nice clean oil would be better than swishing contaminated oil for 20 minutes.
Either way I consider it the same, its still a 20 minute continuous cycle. I set my timer and it takes me less than 10 seconds to spit and put clean oil in and I feel better doin it.