And I doubt doing the iptables-save routine will actually save the tc rules.
I may be wrong... but...
You're correct. iptables-save only extracts the iptables rules.
I don't know what's needed to get the tc stuff, perhaps "tc show". You'd need to parse the output into something that can easily be restored, perhaps the same same script of tc commands you'd use at boot time. Might be a good thing to bugzilla as an enhancement request for the iproute package (which owns the tc command).