Higher current output from transformer?
In short, no. If you want more current into a load, you must decrease load resistance. If you want more current through that transformer and start pulling more than what it's rated at, it will overheat, the insulation will melt, the wires will short, and you'll end up with a nice big, smokey, smelly brick. (I would know, I've done this a couple times before.)

The only way you could possibly draw more current from the transformer than what it's rated at (20VA) is to take it apart, take out the secondary winding wire, replace it with thicker wire while still maintaining the same number of loops so that you maintain voltage. Even then, I doubt you'd be able to fit that many loops in there with the thicker wire because the transformer core itself has been designed from the ground up to support only 20VA. You may be able to get marginal increase in current by that technique and keeping it actively cooled. Even that would only give you 10-20% increase in current capacity though.

There's no way you'd get the 3.6X gain you're looking for. 

On the other hand, there's no reason why this transformer won't work with your charger. The transformer will supply what it can and the battery charger will consume what it can. It will make your batteries charge slower, but shouldn't cause any problems. The only thing you should ensure is that your charger doesn't try and consume much more than 20VA at any given time. If so, you'll either want to add a low value resistor in the loop to limit the charger's ability to consume current, or you'll want the transformer more actively cooled.