Let's pick off the easy answers first. Do you want the synth mixed with the guitar signal in Output1, or do you want guitar in Output1 and Synth in Output2? From what you said I assume the former. In which case you need an FX block positioned at the right hand end of the Ultra's effects matrix, with no connectors coming into it. The Ultra will automatically connect the FX block to Output1 if the block is in the final column of the matrix. If it's further to the left then you will need to connect it manually. This FX block will allow the synth signal to come in through Input2.
If you control the output level of the FX block with a volume pedal then you can fade synth in and out as you play. This is particularly effective for string and choir pads behind picked of strummed chords. You could use the pedal on the GR33 to do this, but using a separate volume pedal allows you to reserve the GR33 pedal for other effects, such as adding rotary speaker for an organ or adding high octave for strings or choir.
Next answer is about how you route the guitar signal through the GR33.
Option 1 is to connect guitar magnetic pickup output to the GK pickup control with a short jack to mini jack lead. This runs both guitar and synth signals down the multi-core cable into the GR33. It will result in both guitar and synth coming out of the GR33 L and R outputs. You probably won't want to do this because you won't be able to process the signals separately in the Ultra.
Option 2 is the same as option 1, but with the addition of a jack to jack cable from GR33 'guitar out' to Ultra Input1. This enable you to route the guitar and synth signals separately through your Ultra. It also allows you to use the guitar/mix/synth selector. Personally I wouldn't do it because I feel the guitar signal loses its high frequencies
Option 3. Don't connect the guitar out to the GK pickup. Instead run a normal guitar cable from guitar to Ultra Input1. OK, you've got two cables, but IMO the sound is much better. Then you can control the guitar/mix/synth switching and fading from the floor, and continue playing whilst you do so.
FWIW I use Option 3. FCB pedal1 is guitar volume, FCB pedal2 is wah, and I use a separate volume pedal into the back of the Ultra for synth volume. This give me almost all of the control I want. There is one song, "Call Me" by Blondie, where I want to swap from guitar rhythm to synth solo in less than a second. There isn't time to hit both volumes, so I have a specific patch where turning up the synth volume kills the guitar volume.
Let me know how you get on with linking the Ultra and GR33 by midi. I haven't tried that yet, but it's somewhere on my "to do" list.