The problem with your set up is that the VNA doesn't have enough level to drive the LDMOS into the right power level so that you will have to use a driver between the DUT and the VNA for properly drive the DUT.
What happens is when you tune the fixture's narrow band network, you will be matching the DUT to the driver's output impedance which is not a standard 50Ohms. You can overcame this problem attaching an isolator between the driver output and the test fixture input so that you can guarantee the DUT is being matched to 50Ohms.
Another correction I would make is that once you have the fixture's input and output network tuned, you have to take the DUT off the fixture and the VNA should to be connected in place of the DUT. You can use a small piece of coaxial cable to connect the VNA to the fixture's input and output (as seen by the DUT), perform a shift in the phase plane to account for this small piece of coaxial and then measure the impedance as seen by the DUT's input and output. These are the conjugate of the impedances you will use to synthesize the final input matching and output transform network.
Yes, this approach works very well.
NandoPG