Is it possible to measure the dispersion changes at my listening positoion that effected the soundstage? What made the sound more lively and dynamic? Sorry if this is common knowledge, I am ready to learn new things.
It could be various things. Your original speaker placement may have been causing problems with first reflections at the LP. The reflections which arrive very quickly cannot be heard as separate 'sound events' (unlike say the echoes you hear in a very large room) but they are there nevertheless and they merge with the original sound to cause a sort of muddying of the sound. By moving the speakers (or the LP) you may have changed the way this issue is interacting with you at the LP and this could manifest itself as a 'clearer, more dynamic' sound. Also, you toed in the speakers and this may have given you a better on-axis response which would affect the HF, contributing to the more 'lively' sound you heard.
The point is, there is no way sitting here that I can know - I can only speculate. Which is the entire point of measuring. If you had measured your room you would KNOW why the sound was better or worse following your changes. At the moment we can only speculate. It is even possible that the 'differences' you heard were simple placebo.
There are other things that could have caused the effect too - but the point is they are ALL measurable. There is nothing you can hear which cannot be measured (because modern measuring gear has far more ability than the human ear) but there are, of course, things you can measure which cannot be heard (and thus they can be ignored - like the very small differences in distortion specs in amps - if they are not audible then it doesn't matter).
Once you have grasped the purpose of measurement, you are well on your way to seeing how it can help improve the SQ in the room and also why it is false for people to assert that "all they need is their ears".