I don't think a 7wo really needs play time - and I agree that she sounds like she's overtired.
Being out of bed for one hour max is more than enough stimulation at that age. Long enough for a feed, burp, change bum and a bit of a chat with mummy - and back to bed. Anything longer and you'll usually have a pretty hard time getting them back down. The bouncer and the HAB both worked for DS at that age, also swaddling is good for getting them to calm down. Have a look at what else is going on the house, try to darken her room and keep things low key while she's settling if you can.
Day sleeps can really be a battle, hang in there and hopefully she'll get better soon.