It sound like you are confusing the rules of different RTW products that you have been researching. For example some of the Skyteam products have a "single direction with no backtracking allowed" restriction, hence the concern with east/west; none of the OW RTW products have such restrictions. Based on the prices, you are looking at LONEx, which are cheaper ex-Australia, NZ and UK. For JFK origin you would be better off starting in UK, if you can live with the routing restrictions for UK origin (no hubbing through UK allowed, as cannot re-enter country of origin). Also, in showing routings you need to show the actual sectors, for example JFK-AKL is actually either JFK-SYD-AKL or JFK-LAX-AKL or JFK-NRT-AKL, or JFK-NRT-HKG-AKL, etc....rather an important difference, and the routing matters for the fare rules.

You need to re-read the stickies and get a better handle on the fare rules (e.g. OWE has unlimited stopovers per continent except for the continent of origin which is limited to 2 stopovers; OWE also has 4 free segments and up to 2 additional paid segments (6 free in NA), so can have up to 5 or 7 stopovers per continent). The fare rules are complex but allow doing a lot, including much of your wish list, so surely it is worth investing an hour to memorize the rules?