transfer between Linodes using ipv6

That's a link-local address, which doesn't allow routing. You'll want to use your public IPv6 address to communicate between your linodes.

ping6 -I eth0 2600:3c00::f03c:91ff:fe96:fca9 also results in a "destination unreachable" ping result.

By the way, what is a link-local address for if not for communicating between two devices on the same network?

Link-local addresses are mostly used to bootstrap stateless autoconfiguration. The first 64 bits (fe80::) will be predictable and the last 64 bits will be unique to that interface. It allows there to be a sensible source address for neighbor and router solicitations to the appropriate multicast groups.

But that's neither here nor there… obviously, something isn't set up correctly.

First, omit the -I eth0 from the ping6 command. You shouldn't need it. That's what the routing table is for :-)

Secondly, do you have any iptables or ip6tables filters blocking ICMP or ICMPv6 traffic? IPv6 makes significant use of ICMPv6, and it shouldn't be filtered.

If neither of those are it, what are the outputs of "ip -6 addr" and "ip -6 route" ?

Plus, don't forget both machines have to be set up correctly to communicate with each other! Even after you fix the f03c:91ff:fe96:fca9 one, the other one might be broken too. You might want to try ping6ing something else too, e.g. ns1.linode.com or ipv6zombo.com, to make sure that the source's IPv6 works too.