What OS is on the PowerBook G3 and what PowerBook G3 is it?
The Classic Mac OS has never been very great at file transfers. I see the same on my 840av, where although with System 8 you can move data and continue working on other things, it doesn't work well, to the point that, say, entering text in Claris MacWritePro or Organizer won't keep up with how fast I can type.
My solution to this problem back in the day was always just to have another Mac available I can go use.
If this is a G3 that has serial, I wonder if the machine would fare any better if you switched the G3 side to Ethernet and used a localtalk/ethertalk bridge instead, or if (if you need/want to keep using the G3) you switched the system performing the operation from the G3 to the SE so you can still use the G3 while the SE performs the network tasks.