hey whirlbreeze - i complelely understand where your coming from, i used to have this problem.
I have been to see terry griffiths son to help me out, and he has stated, only because one eye is dominant, does not entirely mean you have to play under that eye. I am right dominate, but have always played under my chin center, and i feel comfortable this way. You do not always have to believe what is said in the textbooks, in my expereience is better to get the best out of what you already have, and if you are really serious then u may need to consider coaching to address any small technical issuses.
From what you say the issuse seems to be a loss of concentration. Where you put alot of concentration into the first few shots, you start to feel more natural and relaxed and this can cause you to miss an important aspect of your entire line up routine, and ocasionally, it is not taking that second longer to assess the angle, and put full commitment into it.
Concentrate on putting the full attentio and effect into playing your shots when you play on your own. Try to drill it into yourself so you will do it naturally. It will be tedious to begin with but it will help you concentration. A routine i suggest is to line up the 15 reds between the top and bottom cushion of the table, and pot a red followed by a red until you pot all 15, then line up again and carry on from where the white is. It may seem simplistic but it will require you to concentrate fully as you have the tendency to want to play quicker. You must be strict with yourself though, if you miss a red, set them all up again.
If the problem still continues i suggest you need to approach a coach - but IMO carry on with sighting the normal way, but build on the concentration
All the best mate
Start thinking inside the box - too many people are to busy trying to think outside of it