I second the toy library idea! Have you tried wearing your DD in a sling, so she can see what youre doing, and you still have free hands?
Our DD only went into the JJ and exersaucer once she could hold her head steady and roll. I think she was around 6/7 months. Our physio actually suggested them, as she was favouring one side, and they both make you balance things out.
And she was never in them longer than 20 minutes (if I was DYING for the loo/shower) and usually 5 - 10 mins at a time (while I mopped/chopped meat/made her brekkie)