DHCP Relay not forwarding traffic

My understanding, based on my reading of the RFC, is that you must install a route back to the unrouted network. The problem is that giaddr is used for two things. First, it is used by the DHCP server to determine the source subnet, and thus which IPs are valid to be assigned to that DHCP client. Thus, in your example, giaddr must be 10.10.0.4.

Second, at least the way I read the RFC, giaddr is used as the return address for the DHCP OFFER/ACK, rather than the source IP from the relayed DISCOVER/REQUEST. Thus, your private space must be routed for the returning packets to reach your relay agent. The RFC leaves a tiny bit of wiggle room on this point, but that's how I read it.