No, I park facing the pole. The PA method definitely needs you facing the pole and within 1 degree for successful plate solving. So last time I polar scope align first and then 1-star align and then park - gave me 5' accuracy according to Ekos, then did Ekos PA and got 9" accuracy. I suppose if you park with DEC =0 then you could move it to 90 and it should be ok. It kind of doesn't make sense that it needs to be in park first as long as its point to Polaris, but a couple people just found they had to do that.

One weird thing that happens to me is the next. Perform the polar alignment process with the west slewing option. When it is finished, I make the adjustments it ask me to make. Then I restart the alignment process without touching the telescope but asking it to do it to the east. The telescope returns to its original position... but now it is more out of adjustment than in the beginning....

I don't run PA a lot since I have permanent pier. However, the workflow is simple assuming you are starting from parking position facing north:
1. Unpark
2. Run PA wizard (I select West first time)
3. Make corrections.
4. Run PA wizard again (east this time)
5. Done

Yes, this is the same problem I get. I have to park/unpark before each use.

That is what I do. I have a pier now as well, but I do check it now and then from the comfort of my house
I have seen on occasion what @anofeles is seeing where after running back the other direction, the mount is off about the same distance again. Is this just an iterative thing and I should do another round of aligning in the other direction? When it does this, it is off 2-3 arc minutes. I usually just chalk it up to my mount being a lesser expensive model and go on about guiding, but if I can get it closer, I would sure want to.
@knro how close to 0 does your EQ8 get you?