Short cycling boiler. I'm stumped.

Standard operation with a normal chimney vent

1. Call for heat will power up the primary control and feed 120 V to the orange wire. The orange wire is connected to the burner motor, Ign Oil Valve, Etc. and the flame will light.

2. Call for heat over the orange wire looses power and the motor stops

If the power venter is wired correctly then the sequence of operation is different. 

1. Call for heat primary control sends power to the orange wire
2. Orange wire is connected to T1 on the power vent.
3. Power vent motor operates fan
4. Fan prover switch connects T1 to T3
5. T3 sends power to oil burner Motor, Ign, Valve, Etc.
6. Burner motor operates and flame is established
7. Call for heat is over, and orange wire from primary stops burner motor 
8. Power vent motor continues for post purge timing 

What is happening with your power vent is when you get to step 6. Above, the pressure from the combustion process causes the prover switch to open and stop the burner motor. Then the cycle goes back to step 3 above, once the pressure from combustion is gone.

You need to clean the combustion fan. If you have a Tjernlund, the process is about the same just the terminal designation is different

Just throwing this idea out there. Is it possible that the low water cutoff is shutting off power and causing the short cycling because there is no water pressure in the boiler? The water pressure issue really needs to be addressed.

I would definitely check the expansion tank and replace any automatic air vents before refilling the boiler after the pressure reducing fill valve is replaced.

The leaking probe is probably why the pressure dropped to zero since the regulator is probably not allowing make up water to enter into the system.

The corrosion on the insulator of the probe may give a false positive to water presence should the water leak down below that point.

With the high moisture environment inside the low water cut off box the wiring, relay, electronics may have been compromised causing intermittent behavior.

The LWCO unit and the probe probably should be replaced.

With no valves to isolate it, sadly yes, with system pressure being maintained it will probably leak more.

This advice is gonna suck, but needs to be done.

Order a new LWCO and PRV .

Drain the system when they arrive.

Replace both, purge and go.

Remember. No tape on the LWCO probe, light coat of pipe dope only.

You don't need to put Teflon tape or pipe dope on the union connections to the backflow preventer. I'm referring to the connections to the left and right of where it says "inlet" in the last picture. Those connections should just have a gasket in them. I wouldn't be surprised if the Teflon tape causes it to leak.

The top lever on the Watts 1156 PRV (auto feed) works like this:

• In the upright position the pressure reducer is bypassed and the valve is in the open position and will continue to add water regardless of the boiler pressure. CAUTION: this will add pressure above the relief valve pop off pressure and you may get water all over the floor

• To adjust the valve pressure to match your expansion tank pressure you need to drain some water from the boiler in order to reduce the boiler pressure to about 10 PSI or lower. Do this by letting some water out of the boiler at the boiler drain. You do not need to empty the boiler, just get the pressure lower than your expansion tank empty pressure.
  

• Remove the top cap that holds the toggle lever completely, and that will reveal the pressure adjustment. Remove the center fast fill pin in order to place a screwdriver in the slot

NOTICE: If the fast fill pin is missing, the fast fill feature of the Watts 1156F will not work.

• Loosen the locking nut so you can adjust the hollow brass adjuster screw with a screwdriver.
• Turn the adjuster counterclockwise at least 2 turns.
• Open the manual feed valve to the PRV.
• Listen to hear if any water is flowing into the boiler.
• If there is no flow or when the flow stops read the boiler pressure on the gauge.
• Turn the adjuster screw clockwise until you hear water flow into the boiler and watch the boiler pressure gauge.  
• If the water flow stops before you get to 12 PSI (or the desired pressure for your system) then turn the adjuster Clockwise a little more. Continue this adjustment until you get the PRF to stop adding water at 12 PSI
• Once you get the pressure adjustment where you need it, then tighten the locking screw.
• Replace the small pin in the center of the adjusting screw
• Replace the cap with the toggle lever.  

There is a good video on YouTube that explains what water pressure you need in your boiler. Copy and paste this ULR to your Web Browser to see it on You Tube. https://www.youtube.com/watch?v=D9jtvsXJoGg