It sounds like you may have some bad connections between sections of track, even though they are new. If you have a lighted car (or voltmeter), use it to pinpoint exactly where power drops off. Use a jumper wire from the center rail of a good section of track to the center rail of the bad track and see if it improves the power. If it does, remove the bad section of track and replace it with another section if you have one. If you have no replacement track, slightly bend the connections on the end of the track to make better contact. Worst case, you may have to permanently add a jumper between the two tracks underneath the track sections.
If the new power packs OUTPUT A.C. voltage, you can use the postwar transformer with the new trains. If the new power packs do not output A.C. voltage, then you cannot use it.
Make sure you are using a heavy gauge #14 wire to distribute power to minimize voltage drop between the power supplies and the track.
Larry