Hi Willem,
I just want to know the Q you mentioned is for which network. As we know for L network, the Q is fixed by the input resistance and output resistance. Since you want to match 2.3 ohm to 3.3 -j 3.94, you should include the -j3.94 to your network first, so the matching is from 2.3 to 3.3, the Q is fixed if you still want to matching it by a L network (here the L network contains the -j3.94, the Q is for the entire LC network). If you regard the "L" network between 2.3 ohm and 3.3-j3.94, then the real network between 2.3 and 3.3 is not a L network, thinking about the -j3.94 it is a cap at the right side of C2. Then you say the Q of L1, C1 or C2, it is not fixed by the resistance ratio. This is a problem of how to specify the Q of T or PI network.
If you match 2.3 to 3.3-j3.94 by the network you mationed, then in fact you are not using a L network. You can reduce L1 and C1 to a component if you have a suitable valued L or C. L serials with C, it is nothing, it is still a single L or C, depended by the value of L1 and C1. unless you don't want to L1 affects the DC bias of the right side circuit, C1 is no use.
In fact, all the matching is performed between real resistance, the image part of impedance is absorbed into the matching network. Hope it helps.