2008 Prius Tweeter Connections

About a month ago I installed a pair of Alpine two way speakers from best buy to replace the front stock speakers on the base system. They came with the woofers, tweeters and 2 separate in line crossovers. The way they're supposed to be connected is the woofers receive the full range signal, and from there they have 2 extra terminals (on each woofer) to connect the crossovers to the tweeters.

The stock connection on the prius as I understand it is completely opposite, signal to tweeters first, then to the woofers, so my question is, could I somehow bypass the initial connection by connecting the positive and negative wires going to the tweeters directly to the wires that go to the woofers, and then from there use the terminals on the new woofers to connect the new tweeters?

I know, this sounds really complicated

Any help would be greatly appreciated