Yes, it's a good idea in theory but not in practice. Lava shows no aggression at all toward her nor her toward him but Lava has been peering through the divider looking SO sad because she won't come play with him. She ignores him and he can't understand why he is not allowed to go to her and play. I am quite sure if they were together he would be very gentle and sweet (not that I have any intention of trying that) but eventually they would spawn and then he would do what instinct tells him to do, which is chase away or kill the female to protect the fry.
It hurts me to see the sad look on his face when he stares through the fence and wiggles his hips trying to get her attention.
Lava will be better off in the other tank where he is free to go anywhere in the tank and not be made to feel like a freak being separated from the other fish.
I'm turning the 10 gallon into a female tank. I've already brought home two adorable little girls to add to the 3 I already have. I did some research and talked with people who have female Bettas together. They suggested 5 girls in a well planted 10 gallon with lots of caves and hiding spots. One lady has been keeping female Bettas together for years and said she has never had luck with less than 5. Even three is bad because sometimes two will be bullies and kill the third. They also said odd numbers do better than even, though I have no idea why since I doubt fish can count...
She has several groups of 5 females and has no problems with them.
I went to the fish store this morning and observed for a long while, the females they had together in the large tank. I tried to spot the dominant fish and the least dominant. I chose the two girls whom everyone was picking on and chasing away. One of my new girls has a chunk bitten out of her tail from a very bossy Cambodian female in the tank. She seemed to be the Queen Bee so although she was beautiful, I didn't want her. She was also a crowntail and they are known to be more aggressive. All my girls are Veiltails except Noelle who is part Crowntail. I have a feeling she'll be the bossy one...
I'll observe them and if anyone gets too aggressive and won't calm down after some time, she can be removed and put into solitaire. I have several extra tanks.
The two new girls (who have no names yet) are different colors from the ones I already have. I wanted them to all look unique so I can easily tell them apart. One is white with irridescent turquoise fins and splatters of other colors on her body ,like someone shook a wet paint brush at her, (she's the one who's tail was bitten) the other fish is red. Will post pics when I can.
Hopefully they'll all get along and I can have fun watching them play.
The girls are relaxing in their quarantine tanks while I get the new tank all set up. I have a new cave ornament and more plants.
It will be fun but nerve wracking watching them after I release them all and they see each other for the first time.
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Maybe she'll settle down when she gets used to the new place but right now she's really having a lot of fun. Hard to believe she is the same half dead fish I brought home! She's very healthy now! 
Keeping a record of everything was something I planned on doing anyways so I may as well share what I learn with others. I would make me happy if others learn and are able to rescue cup-dwelling females and give them nice homes in tanks. 