The version of Finale you use must be really ancient!
I've been using the product for some considerable time and I've always been able to use more than 16 channels.
Port 1 has 16 channels, then, if you need more, port 2 has another 16, and so on.
I still use an ancient copy of the Yamaha sequencing program XGworks, from the late nineties, and I've had that with up to 96 orchestral tracks (6 x 16 channels).
And you can always reassign channel 10 to any other instrument, it isn't fixed at percusion, that's just the suggested channel.
Many sequences put a second 'kit' on channel 11.
Maybe it's time for a software upgrade?