Is there a polite way to help a neighbor see how draining she can be in group conversations?
I would argue that one of the definitions of "socially awkward" is not being able to read social cues, and it sounds like your neighbor is completely deficient in that most necessary of skills. However, it's not like telling someone she is a bad conversationalist is as easy as telling her she has spinach in her teeth.
The close-talking is the easier of her two problems. Next time she starts in, take an obvious step backwards and say, "You'll have to excuse me, Dorothy, but I require a little more personal space than that." Then, in any future conversations, you can say, "Remember, I need more personal space." It's probably not a natural or comfortable thing to say, but if she can't take a hint, you'll need to spell it out.
When she corners you at the next block party, give her a few minutes of polite attention, and then do exactly what you've done: make up an excuse and move on. In social gatherings like I imagine you're having with your neighbors, it's natural to talk to lots of people for short amounts of time rather than spend an entire afternoon with one individual. If you see Dorothy cornering someone else, you can provide some relief by approaching and diverting the conversation. Even saying, "I'm going to get a drink. Would anyone like anything?" gives the other person the opportunity to say, "Good idea, I'll join you."
Since you mention sitting around a table with only six people, maybe it's in your best interest to avoid these more intimate gatherings with Dorothy. If that's not possible, or if you really do enjoy her company other than these few eccentricities, think strategically about the seating arrangement. Maybe a game night or some other interactive activity would prevent her from setting her conversational traps. You could possibly even consider having coffee with her one-on-one so that at the next public gathering, you can say, "It was great catching up last week, so I'm going to spend the evening talking with people I haven't seen recently."
If none of this works for you, you can either avoid her altogether or be polite while trying to clue her in: "Dorothy, you have such wonderful stories to share. At parties, though, I think everyone enjoys the opportunity to move around the room. I hope you don't mind the feedback, but I think it would be great for you and everyone else to spread the conversation around."
If you can't bring yourself to say that or if she still can't internalize the message, then keep making up excuses to escape and try giving her a neighborly wave instead of asking how she's doing.