The satalites, well im going to upgrade them with sony bookshelfs.
If you're already replacing the speakers, I would recommend picking up a receiver as well. You can probably find something new for $150 or used for cheaper that would handle your needs.
If you are already connecting to the z-5500s digitally, then you'll have an easy time finding a cheap receiver that will handle your computer tasks.
You'll be able to set the crossover point with a decent receiver and you'll still be able to hook up the Logitech sub to it. With the lower crossover point set at the receiver, your new speakers will get the frequencies you intend to send them and the subwoofer will only be sent lower frequencies from the receiver, so its higher internal crossover point will be irrelevant.
If you're hooking up via analog, you'll need a receiver with a multichannel input. You also may run into issues with the crossover this way, since the multichannel analog input on a receiver may disable its own bass management system. You'd then need to rely on your soundcard to do bass management (if it has this feature).
EDIT: You said you determined that the z-5500 sats were still producing sound at 80Hz.
The z-5500 crossover is set higher, so the signal send to the satellites is progressively weaker as the frequency lowers from the crossover point. At 80Hz, the satellites will still be being sent something, but it's much lower in volume than it would be at 150Hz.
Even if you get speakers that can handle bass better, the z-5500 sub will still be using a 150Hz crossover with them. You could put another filter in the z-5500 sub so the subwoofer doesn't play much above 80Hz, but the satellite amplifiers in the sub will still be sending out signals to the satellites to mesh with the default subwoofer assuming that the 150Hz crossover is still in place.
So, you'll get reduced output from the system in the 80Hz - 150Hz range. The output in this region will not be "0", but it will be less than you want it to be. The satellite amplifiers will not know that you now want them to fully take over the 80Hz to 150Hz range, so they'll still start reducing the output sent to the satellite speakers starting at 150Hz and on down.