LPX is apparently the standard from which ATX was developed, at least in terms of standardized power supply dimensions and most voltages/signals. So the LPX and ATX soft power signals are the same: there's a 5V standby, a PWR ON pin, and a PWR GOOD pin. The 4400 has 5V SB and PWR ON (and a GND) in that little 3-pin connector while PWR GOOD is on one of the main power plugs as you've noted previously.
On that -5V issue, it's possible the 4400 doesn't use it, as mentioned above. Try omitting it to see if the machine boots and runs stably; if it doesn't then obviously it's required and you'll need to provide it somehow, but temporarily not having it isn't going to blow anything up so there's no harm in trying.
If there are other wires that aren't used on the new power supply, such as the extra 4 pins on the main connector or the 12V CPU aux connector, you can safely ignore them; just because they're provided doesn't mean they need to be utilized.
Try opening both power supplies. Most of the good ones will have the voltages/functions listed on the component side near where the wires go into the board. I haven't done it yet but I was planning to completely desolder the harness from a modern 20+4-pin ATX power supply and install a harness from my Umax S900's defunct power supply in its place. The Umax's PS is a weird non-standard thing but it's electrically similar to ATX so there are corresponding points in the replacement ATX unit for all of the required wires. By doing this there are no splices or vestigial connectors hanging around (such as the CPU 12v connector, SATA connectors, etc) and everything is still the correct length.
On that -5V issue, it's possible the 4400 doesn't use it, as mentioned above. Try omitting it to see if the machine boots and runs stably; if it doesn't then obviously it's required and you'll need to provide it somehow, but temporarily not having it isn't going to blow anything up so there's no harm in trying.
If there are other wires that aren't used on the new power supply, such as the extra 4 pins on the main connector or the 12V CPU aux connector, you can safely ignore them; just because they're provided doesn't mean they need to be utilized.
Try opening both power supplies. Most of the good ones will have the voltages/functions listed on the component side near where the wires go into the board. I haven't done it yet but I was planning to completely desolder the harness from a modern 20+4-pin ATX power supply and install a harness from my Umax S900's defunct power supply in its place. The Umax's PS is a weird non-standard thing but it's electrically similar to ATX so there are corresponding points in the replacement ATX unit for all of the required wires. By doing this there are no splices or vestigial connectors hanging around (such as the CPU 12v connector, SATA connectors, etc) and everything is still the correct length.

