I would agree with your assessment having lived in Wimbledon (ministers) for a year now.
Wimbledon Village is like Happy Valley in HK - posher shops (but not what you would buy day to day), older crowd, not so convenient as up the hill from Wimbledon station. Also more expensive.
Wimbledon Park - lovely feel. Some nice little shops but the district line is just too infrequent, esp on the weekends. So I wouldn’t like having to rely on that one line. Wimbledon Park itself I personally find disappointing. The paths are soooo narrow. I would compare it to Tai Hang.
Ministers - love the proximity to shops and restos on Broadway, and equidistant to Wimbeldon and South Wimbeldon stations. For offices in Canary Wharf, South Wimbledon northern line change at London Bridge is better option than SW rail to Waterloo then change to Jubilee. South Wimbledon being second stop on northern line you are guaranteed a seat. SW rail Waterloo interchange is mayhem. However, depending on the house and road, houses are more narrow and long. Gladstone has bigger properties also reflected in price which is likely above your budget.
South Park Gardens - in the 1-1.2m price range you are looking more Clarence Road, Effra Road etc. again same as ministers, narrow terraced houses and even further away from train stations. So slightly cheaper than Ministers. Past Haydons Road playground, personally feel it’s less nice.
Battles - it’s like the Ministers, but closer to South Wimbledon tube and further from Wimbeldon, hence slightly lower price point. But quite similar to Ministers.
The Australias - having lived in Wimbledon, this is what we liked best. Edwardian houses mean wider houses and around 1500sq feet. Agree with others that it’s best to find something that has been extended loft/kitchen as labour and material is getting more expensive. At 1.2m, you would be looking at a done up place similar to your link above at Boscombe road. And if you are chain free, that puts you at an advantage. But beware of old roofs as they will need replacing soon. It’s quiet, leafy and more younger families now (catchment for Pelham primary and Rutlish I believe).
good luck with your decision and the move!