If you think you have equations that will resolve the problem you do not need the actual values; just give them names. Like "short here and there and we have this and that in parallel, let us call that value K", etc. then with the givens K,L,M,N you can go on to resolve and give us the final result.
But, furthermore, if you look carefully at the OP you can see I already short circuited some terminals and gave the values I obtained which, indeed, simplified things but not enough to make it easy. The values were right there all along.
Sorry, I don't have time to help you doing a simple calculation, to give results that are only useful to you. But I have time to help everybody who is facing a similar problem to yours.
In order to simplify the equations you can:
1) Short circuit some terminals in order to have the parallel of any two resistors in the circuit.
2) Write the equations in terms of conductance, not resistance, so the equations will be simpler.
Once again, more complete:
Calling the conductance G1=1/R1 and so on, you can do the following:
1) Shorting 1 with 4 and 3 with 2, measure between those two terminals: Gx=G1+G3
2) Shorting 1 with 3 and 4 with 2, measure between those two terminals: Gy=G2+G4
3) Shorting 1 with 2 and with 3, measure between those terminals and 4: Gz=G3+G4
4) Shorting 1 with 2 and with 4, measure between those terminals and 3: Gt=G2+G1
5) Shorting 2 with 3 and with 4, measure between those terminals and 1: Gw=G4+G1
6) Shorting 1 with 3 and with 4, measure between those terminals and 2: Gu=G2+G3