Hey Neighbor,
A few thoughts:
1. I realize that Thailand is last on your list (and IMHO it should be first
), but in any event the best way to get there (or elsewhere in much of Asia) is using your AA miles CX F, which is one of the best airline experiences you can have. My wife and I have done it on a couple of trips...among many fine features, for drinks and dining you two can sit across from each other in the same suite for a very romantic meal...like the Orient Express at 30K feet. Plus fantastic CX F lounges in HKG when in transit. You almost have AA enough miles yourself to do that for the two of you. Counting your wife's miles, you're well over the top. Check the CX, AA and Trip Report forums for reviews, photos, etc. re CX F.
2. Best option for South America is using AA miles for LAN J, which I haven't flown yet (we're doing it to to Peru later this year), but hear great things about.
3. Beware of flying a BA award to or via LHR, as it tacks on very high $$$ fees. I forget whether using in AA miles to fly BA (which otherwise is a very nice choice to Europe, such as if it's a revenue instead of award ticket) costs as much as if you use BA miles, but it's something to look into. In fact, look into whether any award connection via LHR costs significantly more than through other cities.
4. Especially in view of #3, UA J connecting to LH in Europe might in fact be your best bet to Greece or Turkey. Sometimes LH F opens up a week or so before a flight, so if you're open to changing flights late in the game you might keep this in mind as LH F (including its F terminal in FRA and its F lounges) is another very special experience. But in J, UA trumps LH.
5. If connecting on UA transatlantic to LH intra-Europe, LH's MUC hub is much nicer and easier than FRA...if you have that choice in your routing.
6. Not sure about award availability, but UA J to SA J to get to South Africa is a nice option, as SA J is great and has great legroom. At least when we did it a few years ago, there was practically no SA award availability from IAD or JFK, so we connected through LHR (but you can connect via other European cities as well).
7. As with Greece and Turkey, if you can snag LH F all or part of the way to South Africa you'll be in for a treat.
FWIW, of the airlines I've mentioned, in J I'd rate CX>SA>BA(but beware those fees)>UA>LH>AA. For F, I'd rate CX>LH>BA>UA>AA (Haven't flown SA F and am not sure they still have it.)
Especially given how many UA, AA and MR miles/points you have, I'd save my SPG points for hotel redemptions, especially for when you can find the great cash + points deals Starwood properties sometimes offer.
Happy trails!