If your machine is similar to the one in the pictures than your problem is not the pillow blocks, unless you have some with manufacturing issues or badly aligned. The problem is most probably the fact that it is a moving gantry design. I am using similar supported round rods with open end pillow blocks and have absolutely no problems at all, get very high speed and accuracy and very happy with it. The big difference is that I decided to build a fixed gantry, moving table type of machine, not what is most popular, the moving gantry type, which is more difficult to align, difficult to get the speed and accuracy right and is easy to get gantry vibrations and misalignment with.
The above parts list is fine, with a few exceptions.
Don't use ANY unsupported round rods (items 6 and 11). Why do you think that 25mm unsupported round shafts will be better than 16mm supported ones? They are NOT better.
What is the item 8 exactly do and where is it located? I don't understand that and the purpose of it.
Consider moving table fixed gantry design, and also remember that slaved motors can be a problem as well, they might cause the same sort of issue with accuracy unless you have very accurate ball screws and nuts. I am using 1605 on all three axes and have only one on the Y also, which is my table. My frame is build mainly with 45x90 and used 30x60 for some parts. Also already now make a decision about the electrical parts, driver and controller software. Talking about electrical parts... I'd replace the Kress with a real VFD controlled spindle Even an air cooled 1.5kW would do better than that Kress, which really is only a high quality angle grinder. Even if you are not willing to throw it away, design the Z so that one day when you decide to get a real spindle you could easily install it. The Z is the most important part of a machine. If you get it right half of the battle is won, but the Z includes the spindle as well.
If you want to have a look at my specifications you can visit this post:
https://adapting-camera.blogspot.se/...nt-status.html
I don't have a real build log, but on my blog you can find many posts regarding my building progress.