First, I'd have her clean the messes up after her accidents. Make it a long laborious process so she can't get back to playing quickly. Don't get angry but show your disappointment, "Ohhhhhhhh, another accident? Now you have to stop (whatever she's doing) and clean yourself up." Give her gloves, have her place poop in the toilet and flush it, rinse and wash the panties and pants out in the sink with soap, (my sister had my nephew use Zote which is a laundry soap,) put her clothing in the laundry, clean herself, wash her hands with soap and put on clean undies and pants.
Also, since she doesn't mind the wetness get her some plastic pants to put over her panties so she can feel the wetness and poop more. When it spreads throughout her clothing it's not as uncomfortable as being right next to her skin and icky.
Since she's good on weekends when you're out and about with no extra panties why not try what one mom posted on here a while back? She puts her son's clean underwear where he can't see them, then tells him he has to wait while she does a load for clean ones. She has him wear a long t-shirt for privacy, but he waits by the washer and dryer (his choice) while they're going, and she says things like, "It's too bad you had that accident. You're missing (whatever he was doing.)" She said his accidents are getting fewer and far between.
I would also go back to potty training 101 and a "potty time" schedule, so she has to stop whatever she's doing for that as well, just keep up your 20-minute rule. That combined with cleaning up her accidents will take her time away from playing or watching TV and will hopefully begin to bother her and prod her to be more attentive.
Make a chart to put stars stickers on after an accident-free day, and show her how if she goes a week (or 10 days in a row) without any pee or poop accidents she will get a bigger reward. Choose between purchasing something she'd like and put it up high where she can see it but not get it until she completes the goal, or a promise to buy a certain toy or go somewhere she likes when she reaches that goal. If she has an "accident" you start over, with her still getting a daily sticker for no accidents, but the goal for the bigger reward starts over. This may work better than going to bed early because it will reward her positively.
With wearing her panties until she's red I definitely would have a consequence. If you make her responsible for changing when she's had an accident and rinsing wet or soiled panties and clothing out, she would know when it needs to be done. I'd sit her down and tell her this is unacceptable behavior and that if it happens again she will have the consequence of (no playing time, going to her room and sitting on her bed with no toys or books, no TV, losing a privilege, whatever you choose that will make an impact on her, since going to bed early has no effect.)
If she's excited about going to school tell her that the other children will make fun of her if she smells or cries because she hurts in her potty area or they see she's had an accident, it's sad but true. If she has friends that are potty trained with no accidents have her spend ample time with them, peer pressure can be a great thing.
Hope she stops the "accidents" soon : )