I know this is an old post, but I am posting here anyway in the hopes that I can still help someone who has the same question.
After searching extensively for a way to do this, I came across some relevant C++ code that appeared to do the trick, so I wrote a small command line utility to achieve pixel-perfect adjustments to multiple monitors. It also only needs to be run once and is persistent through reboots.
The command works like this:
dpedit.exe <monitorIndex> <X> <Y> [<monitorIndex2> <X> <Y> ...]
For instance, I figured out that in my monitor setup, my secondary monitor was near-exactly 21 pixels lower down than my primary monitor. So, I simply ran the command
dpedit.exe 2 -1920 21 to position my 2nd monitor 1,920 pixels left of and 21 pixels down from the first, leading to the result pictured below.
Monitor positioning result because I can't embed images yet
Feel free to check out the tool here: DPEdit