|First tip is to get yourself some fleece/stay-dry liners. They're super easy to make, just buy some cheap polyester fleece and cut to the size/shape you want. That's it, no sewing because fleece doesn't unravel. You can also buy some non-fleece stay-dry liners from ME. At least this way you can ease your mind about wetness at night and reduce the risk of diaper rash.
Another tip, don't forget that even in disposables, she's still sitting in urine all night. We tend to forget this kind of thing (I do it too sometimes). Sure there's a stay-dry lining that makes baby feel the wetness less, chemicals to absorb 50 tonnes of urine and perfume to make it all smell good (well, to some at least, others can't stand the smell), but it's still urine.
For diapers I'd say you're fine with what you have, just add some liners and that should do it. Thin cotton liners probably aren't enough unless you add a ton of them. Which is just fine of course, don't be afraid to pack in as many as are necessary. That said, as long as the diaper isn't leaking and she doesn't get a rash, then it really doesn't matter how wet it is in the morning. Healthy skin and no leaks are all that's really important in the end. Some people (like me) like to really stuff their nighttime diapers, just for mom's benefit when removing the diaper in the morning, but that's personal preferance.
If you do want to buy something different, you could try bamboo diapers/liners. They absorb more so the diaper/liner is trimmer, which can be nice for nighttime so that you get the same absorbancy while reducing the bulk a bit (though a big bum never hurt anyone, no matter how funny it looks!). Some also like to go up a size for nighttime (like if they normally use a small Sandy's they'll use the large for nighttime). She might be a bit young for that yet (cause the larges are highly unlikely to even remotely fit her) but just for future reference...
And finally, if you do want to use up those disposables but are sick of blowouts/leaks, try putting a cloth diaper and/or cover on top of the disposable. The diaper will help absorb leaks if you get them and the elastic from the cover will help with blowouts...