Tubes can be wired up in all different kinds of ways, and they will often still work, but perhaps not sound so good.... lol
Taking a look at what you have found....
C3G 6AK5
1 heater ---------->3 heater
2 grid 3 ---------->2 and 7 cathode and grid 3
3 plate ---------->1 grid 1
4 grid 2---------->Not connected to any 6AK5 pins
5 cathode ---------->6 grid 2
6 grid 1 ---------->5 plate
7 cathode ---------->2 and 7 cathode and grid 3
8 heater ---------->4 heater
Obviously, you should switch things around so that grid 1 and the plate are connected properly. And then, connect grid 2 in each tube. And since the C3g pins 5 and 7 are tied together inside the tube, you can leave 5 not connected. Also, it is useful to know that 6AK5 pins 2 and 7 are tied together inside the tube.
You have to remember that both the C3g and the 6AK5 are pentodes. And therefore, it is necessary to convert them into triodes. This is done by tying the extra grids, grid 2 and grid 3, to either the plate or the cathode.
In the EF95 setting, your amp expects to see a 6AK5 with the cathode tied to grid 3. And on the circuit board, the amp will tie grid 2 (pin 6) to the plate (pin 5). And thus, you have a triode-strapped 6AK5.
So first, we need to strap the cathode and grid 3 in the C3g together. And the adapter you have does this by tying them to the strapped cathode and grid 3 in the 6AK5. Second, grid 2 of the C3g must be aligned with grid 2 of the 6AK5 so that the LD can strap grid 2 to the plate. Once that is done, it is a simple matter to make sure the heaters, cathode, grid 1 and the plate are lined up correctly.
So this should work:
C3G 6AK5
1 heater ---------->3 heater
2 grid 3 ---------->2 and 7 cathode and grid 3
3 plate ---------->5 plate
4 grid 2---------->6 grid 2
5 cathode ----------> not connected
6 grid 1 ---------->1 grid 1
7 cathode ---------->2 and 7 cathode and grid 3
8 heater ---------->4 heater