That's an excellent thought. I tried it at your suggestion, but no joy.
However, your input was helpful because it made stop looking for a missing extension or for something obviously wrong with the commands.
After much trial and error, I did find the relevant difference between Devuan and TC: For TC I decided to go with a privacy-friendly (i.e., no logs) DNS provider and added this line to the top of /usr/share/udhcpc/default.script:
dns="91.239.100.100 89.233.43.71"
Removing the line made the speed problems go away. Very strange. Why would manually setting the DNS provider (rather than accepting whatever the DHCP server provides) cause a dramatic decrease in speed?