Okay - first let's make a few things more clear. The clicking you are describing typically comes from voltage being modulated by the LFO interfering with the audio signal. This is not a typical issue with this circuit; of the hundreds of successful builds, there have only been one or two builds exhibiting this symptom, and those are typically only clicking when the circuit is engaged, not when it is in bypass. Therefore, the actual circuit design is not likely at fault; it is more likely that something in your particular build is causing this. Since your symptom arises only in bypass, we can assume that LFO noise is being transposed onto the audio signal in bypass as it runs from the tip of the output jack, down through pcb traces to the footswitch, across the footswitch, and back through the pcb to the output jack. Placing a buffer on the signal prior to the circuit would lower the signal impedance which in this case appears to be insulating the signal from the LFO clicking. The Rev 1.1 mods changes the polarity of the input buffer; it does not add a buffer to the circuit, nor was it designed to reduce LFO noise. So don't worry about that.
Moving onto what we can do to fix the problem, the most obvious thing is this; the vast majority of working builds with no issues do not have the large amount of solder build up on the component side of the pcb. Therefore, it would seem that with your build having so much solder built up around almost every connection, that is causing some cross-talk between the LFO circuit and the audio circuit somewhere. However, fixing that is probably impractical because there are so many solder joints on this pcb and the components are very crowded; it would likely take hours and hours to wick or suck the solder from so many joints and attempting to do so would likley result in damage to some components and maybe the pcb itself. I do suggest you try though; remove all of the ICs from their sockets, make sure your iron tip is clean, shiny, and hot, and reheat each joint from the solder side of the pcb to see if you can draw some solder back away from the component side. You might get just enough separation to kill the noise. But don't leave the iron on any one joint for too long so you don't do any damage to the components.
If that doesn't work, you can try moving the input and output wires. First, remove the wire from the tip of the input jack to the input of the pcb, and remove the wire from the pcb to lug 4 of the footswitch. Replace this with a single wire from the tip of the input jack straight to lug 4 of the footswitch and route it away from the pcb. This will get the input signal off the pcb and away from any interference it might be encountering there. Even better, if possible, use shielded cable for that connection and ground the shield to the middle lug of the input jack. If that doesn't fix it, do the same thing with the output; remove the wires from the tip of the output jack to the pcb, and lug 8 of the footswitch to the pcb, and replace them with a single shielded cable from the tip of the output jack to lug 8 of the footswitch, grounding the cable shield to the output jack ground. Doing this should isolate your bypass signal from being affected by the LFO voltage swing.OL CIRCUITS
has a nice tutorial on using shielded cable.
A third fix is obvious; just keep a buffer on this pedal. There are a few reports from other builders that placing a buffer before this circuit reduces some loading and makes it perform better. If you are only using an AC power supply and no battery, you should be able to fit the mini buffer circuit in the battery compartment (or do a search for Stephen's micro buffer - it fits there). All you need to do is run the input jack to the input of the buffer, the output of the buffer to lug 4 of the footswitch, connect the buffer to power and ground, and you have a buffered signal both in bypass and effect mode. Since you are using a true bypass strip for this pedal, you'll still get true bypass from the strip and the buffer in the chorus pedal should cure the clicking in bypass mode. However, I suggest replacing the input and output jack wiring first to see if getting the bypass signal off the pcb cures the problem first.