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Craig
Your pursuit is a noble one of which I approve, however I feel obliged to observe the steepness of the road you have set out on (for others interested as much as anything).
Firstly, the reason the textbooks take particular approaches to QM is because decades of attempts to do it other ways by very smart people (eg hidden variables) have come up largely empty. Conversely, decades of analysis and experiment support these approaches. Now, of course that doesn't totally preclude some fundamentally new understanding, however the opening is very narrow. Anything new has to (a) agree with all confirmed experiment to date, and (b) offer up a meaningful difference which can then be confirmed in some objective way. Certainly at the outer edges of particle physics this is not only possible, but arguably inevitable. On the core of QM, though, it's a very tight squeeze. As per comments on Schrodinger/Heisenberg equivalence, simply re-arranging the maths doesn't count, as we already have that.
Finally, I thought I'd clarify the issue of correspondence between QM and classical. This is in fact a directional issue. QM taken to a large-scale limit confirms and agrees with classical physics (or we'd have trouble explaining why civil engineering works) - no conflict. Not the same the other way, though. Classical applied to small-scale phenomena (eg atoms) fails spectacularly, and while semi-classical approaches can sometimes be useful, they clearly fail to capture something essential at that scale, and not for want of trying.
Anyway, enjoy exploring.
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