Greetings George,
You come up with very interesting topics!
IMO,
When a DNA profile is done, only a few characteristics are checked. So I'm betting that in the future when they can check more points more often that they'll find  that DNA changes after some 'transforming' experiences.
For example, don't you feel changed after a truly spiritual experience, like an answer to a prayer or an NDE or OBE? If DNA is anything close to an imprint of our essential selves,  it seems like it would have to change.

I don't believe we can keep the same DNA every time we reincarnate.
As Antwnhs has very well put it, we are not our body. We just use the body as a vehicle and changing geographical location, gender and race everytime it would be impossible to keep the same DNA.
Previous lives experiences affect the soul but not the body. For example, someone healthy may develop a pain in the arm at the age of 30 for no treason at all. In cases where this has been investigated through past life regression, they found something happened in a previous life in that particular arm and at the that precise age.
After the regression the pain stops. If it was a DNA thing the pain would not ease, and the condition would repeat itself.
This is what I think.

Peace.

SC.