OK.
The GZ34 is in its socket.
The SB Switch is open.
The KT66 is in its socket
You have about 6.0 VAC on the heaters, Pin 2 & 7
That sounds normal

With the SB open you will probably have 0 VDC on pin 3 & 4.   You will not see any high voltage until the SB is closed.  That seems OK

Pin 5 is the control grid and that is where you should see some kind of negative VDC.  Maybe something in the range of 0 to -50VDC.

When you measure between Pin 2 & 7 of the power tube socket, with no power tubes, do you get 6 VAC ?
It is normal to have continuity on the heater pins of the tube, 2 & 7.
Is there only a problem when the SB Switch is closed?

The gap is between 5 & 7.   The link below has some info and a picture that should help.

http://tdsl.duncanamps.com/pdf/kt66.pdf

You are really making me work for my money today.... Pentode and Tetrode basically refer to the number of grids, three and two respectively.   The heaters are fundamental in making the tube function, but it is really the control grid (via the bias circuit) that turns the tube "on" and "off".
I kind of understand what you are doing with the pliers and wire.   You have the tubes out of the sockets, and jumper in between the tubes and sockets with wire.   Is that correct?
When you disconnect either Pin 2 or 7, the "short" goes away.   But does the short go away on both tubes and both sockets?    This is getting kind of confusing, but it starts to sound like you have a bad tube, or you have the tube socket(s) mis-wired.

Yes, 2 & 7 are your heaters, so continuity would be normal for those two pins.
Is this a new problem you are having now?    If so, maybe you made a mistake when you hooked up the new SB Switch, and reconnected the tranny wires, and is there also the first filter cap involved with all of this also?  To put it simply, double check any of the work/wiring that you did just recently.

Yeah , it is normal to have continuity on the secondary.   When you measure the primary that is where you should see resistance.

Congratulations!!!
Glad you found the problem.  But where was the SB going to ground?

   What if you measure from Pin 8 to the bare chassis or any other ground connection?   0.4 ohms is the same as 100% continuity.   Is it possible that your rectifier socket is grounded?   Maybe a solder bridge between Pin 8 and the chassis.   Can you desolder the 5.0V wires from the Recto Socket and measure each of those wires to ground.   I hate to think your brand new PT is shorted.   It happens, but not very often.

I am sure Ceriatone would tell you if you ask them.   With that said, I think they are made by these guys.....

http://www.promitheusaudio.com/transformers.html

Well this has been a long one.   Let us know what happens with the new Recto!!!!!
Good Luck

I assume you are using the correct voltage for your country....
If you are measuring the SB Switch when it is open, and there is 0 volts on either post of the switch, that is the same as going direct to Pin 8 of the rectifier.   
So, you are saying there is no voltage on Pin 8 of the rectifier tube?
Also, does the 500 MA fuse blow while the SB Switch is open?
You either have a bad GZ34 or you have something wired incorrectly.

This is getting a little confusing.....
The cap/diode situation on the rectifier tube is a modern day upgrade.   Metro does not show it because it was not original to the 1962 JTM-45.    Whether you use it or not will have no effect on you amp, assuming they are properly connected.    If you are having problems, I would disconnect them for now.   If you email Ceriatone, Nik will explain their purpose to you.
To clarify, when a SB Switch is "OFF" the amp is in normal operating mode.   When the SB Switch is "ON", your amp is not passing signal because there is no HV to the plates.  Regardless of that terminology, you should see HV on the SB switch where it is connected to Pin 8.   You say 325V.  That is assuming you are measuring across an open switch, or if the switch is closed the reference would be to ground.   If you are measuring between Pin 8 and the first leg of the SB Switch, the reading will be zero, or close to zero volts.
What reading are you getting on the SB Switch?

As wyatt says, it is probably a wiring mistake in those areas.    Double check everything very thoroughly.
As far as extra diodes..... are you talking about the 0.01uf snubber caps on Pin 4 and 6 of the rectifier tube?   Those are just a in-rush protection device.   A modern day upgrade you might say.   Not crucial, but a good safety to have, just in case.
What you see between Pin 2 and 8 is normal.   There should be continuity there.
Good Luck

I would wire it just like Nik shows on the Layout.    Don't let the DPDT switch confuse you.   It is two separate switches side by side.   If your amp came with the fuse wired to the center position, then the Transformer/PL would need to go to the top or bottom.    It does not really matter, just so long as you keep the Hot (fuse) lead on the opposite side of the switch from the Neutral (0 transformer line) lead.   The Hot and Neutral should only meet via the transformer, not via any other connection such as a , switch, resistor, fuse, etc. etc.
Just imagine the electron flow coming from the wall, into the AC cable, into the fuse, into the switch, into the transformer, through the transformer, into the Neutral Lead (and whatever it might be connected to) back into the AC cable, and then back into the wall from where the electrons came.
In the midst of all this electron flow, the Primary of the transformer gets energized.   Then from mutual induction, the secondary is energized, and that gives you all of your High Voltage 290V x 2, 3.15V x 2, and the 5 volts for the rectifier tube.
Now that I have over explained everything, do you have a digital meter?   If so, you can teach yourself how that switch works in 2 minutes.
Good Luck

I think you have kind of already answered your own question.   But just to make sure...... The Brown/White ties to the Brown, and the Black/White ties to the Black.   They become your Neutral and Hot leads.   They tie together for 120 volts.   That is the important question.   Is Your Mains 120 Volts??   If so, then proceed.   Wire it just like in Nik's layout.
Hot from the wall goes to center of fuse, out the side of fuse, and over to the top of switch.   Center of switch goes to 120 of transformer and also over to pilot light.
Neutral fro the wall goes to top of switch.   Center of switch goes to Zero line of transformer, and also jumps to pilot light.
As you say, the Purple/White is not used.   Coil it up with a tie wrap.   Cover the end of that wire with shrink tube or electrical tape.   Even if you think there is no exposed copper, Cover It Anyway!!!
Because that transformer sees duty for more than just 120, there are some extra wires to deal with.   Just follow the Westlabs instructions.    Once you have the wires twisted together, consider them one wire.   Does that make sense to you?