I am in the middle of two AONE3s, the details of which are as follows:

AONE3 #1 (ex-BOS): I have flown BOS-LHR-SIN-BKK
AONE3 #2 (ex-BKK): I have flown BKK-HKG-JFK

Here are my parameters: I want to use AONE3 #2 to get back to BKK (where it will terminate) and then use AONE3 #1 to get back to BOS (where it will terminate). Forget the itineraries that I chose when I purchased the tickets; I chose knowing that I would later pay the fee to restructure the itineraries. My goals are to (1) go to interesting places, (2) maximize segments and mileage, and (3) fly on the best flights (such as the CX HKG-YVR-JFK flight, although I'd love to hear if people prefer the non-stop), except for the transatlantic flight on the AONE3 #2, in which case I want to fly AA if departing from the U.S., or BA if departing from Canada, in order to earn AA miles. As to point 3, I want to fly from or to JFK on my transcon segments in order to sit in the F cabin of AA's 762s (or, better yet, sit in the F cabin of QF's JFK-LAX or LAX-JFK flight, if that's possible).

Based on my limited (but not beginner) knowledge of RTW rules, it seems to me that I need to (a) first maximize the North American segments of #2, (b) then fly the transatlantic segment of #2 and maximize the European segments of #2, (c) then fly a Europe-Asia segment on #2, avoiding BKK until I've maximized the Asian segments, (d) then use the remaining Asian segments on #1, (e) then use #1 to fly HKG-JFK on CX, and (f) then use the remaining North American segments of #1 before returning to BOS.

I'm open to suggestions: how to people suggest I reconstruct my itineraries? Assume that I am willing to purchase the maximum number of additional segments possible.

There isn't much to optimize or choose from given that you are on an xONE3. You can only do Asia-NA-Europe and 17 segments, so have to buy 3 additional segments to max it out. I personally think HKG-YVR-JFK is inferior to HKG-SFO or HKG-LAX but everyone has different considerations and the differences aren't really that great. As you are collecting in AA the thresholds in segment length don't matter to you, which eliminates most of the routing fun. What you can do depends on the season when you will be flying, for example sometimes LAX-SXM operates as a single flight number (but not the last time I looked). LAX-SJU nonstop on a 763 is a good flight, but only operates 1 or 2 days a week. Remember that NA includes everything in the Caribbean and north of Panama -- which can make for some interesting destinations but not particularly good flights. As for going to Europe, the rule is to leave from west coast (makes for a much more pleasant flight). If you need to credit that to AA, as you suggested, then JFK-YVR-LHR would be the best use (alternative is MEX-LHR or even one of the Caribbean routes on BA).
I suppose you could pay the differential and convert your AONE3 to AONE4 and add SA, that might be cost effective. I personally think the xONE3 are poor value compared to 4 or 5 continent (even with the 20 segment limit) if you are trying to maximize FF earnings.