There is a way. Use the high-level speaker input/outputs on the subs. Basically, run speaker wire from the receiver's left and right speaker outputs to each sub. Then run speaker wire from the high level output from each sub to it's corresponding speaker, i.e. left or right. In the receiver's setup menu, turn the subwoofer off. Leave the subs crossovers at their highest setting.
Before you do that though, one thing that concerns me is your description that the subs are moving and a lot of air is coming out of the ports. It's possible that all that movement and air is simply the result of distortion rather than controlled audio. Try running both subs at 1/4 volume or less and/or vary the volume of each sub, i.e. run one at 1/8 power and one at 3/8 power. Also, make sure that the sub output level in the receiver is at zero or below to limit distortion at the output. A level of -6 on the subwoofer output may cut distortion from the receiver. Just turn up the volume on the subs to compensate.
I think the OP's problem is most likely caused by an impedance miss match.
His four outputs from his receiver, I bet are all connected in parallel, and not buffered. They should be buffered, but seldom are on domestic equipment.
If his Sony has an unusually high output impedance, and his subs have unusually low input impedance, than that would explain the OP's problem.
The input impedance is not specified. However when using two subs the input impedance is halved. It is quite likely than when using two subs, he only has a miserable clipped signal, at the subs.
I bet if he buffered the two sub inputs his problem would be resolved.
His options would be to build a couple of buffer amps, or use a cheap mixer as a buffer.
Purist approaches require that buffer amps always be used, rather than a Y connection. I know we usually get away with it, and I do it on occasions. However if it is a permanent hookup, I buffer.