NE1 ever upgrading wiring using a relay to the blower motor?

Ditto 67Dart273, can't be your alternator since it should run for an hour off the battery alone. The alternator serves only to recharge the battery.

You would need 3 relays to bypass the switch for low, med, & high. That wouldn't help if a drop to the dash still exists. In all my 60's cars I use a relay for the blower high position only. That keeps the valuable L-M-H and electro-pneumatic switch (factory AC) from melting. You probably don't need that for L & M positions since they switch in a series resistor (in your air box). Don't keep using it if your blower is slowing way down, until you fix it. Motors draw very high currents when they stall.