Greg, you say, in gear, wide open throttle (not turning the wheels) your max RPM is 1650.
MEngr asked (and it is my bet he was looking at the specs):
Is the engine's max full load speed at 2300-2600 RPM and the no load speed at 2800-3000 RPM?
your numbers are; "Rpm's at full throttle in netural are 3100 rpm's, [engine good] In reverse and forward with brake held at full throttle is 1650 rpm's".
[since it should be 2300 rpm, and you only see 1650, I stick with my wag that you need a torque converter].
Bite the bullet, pull the trans, change the trans soft parts (clutches, gaskets and seals) and a reconditioned torque converter.