Of course this one is $1217, so maybe not really practical at this point. But the idea is sound enough.
However, a normal AGM battery in good shape should start your bike without any help. The other day I started a '74 Z1 with ~1250cc and ~12:1 compression with a 1/2 size battery because that's all I happen to have handy. I did maybe 6 starts before it noticed it start to slow down.
If you're having trouble with slow starting, you either need a new battery, to check your charging system, or do some work on your harness.
'78 Z1-R in blue, '78 Z1-R in black, '78 Z1-R in pieces
'95 GPZ1100 (sold) , '00 ZRX1100
I'm kind of a fan of the K.I.S.S. method (keep it simple stupid).
Inserting another device in the path is just another thing to go wrong.
I'm a fan but my electrics tend to be more rube goldberg.
I've had relays go bad when I could have just increased the wire size and not had the issue.
I would increase your wire size first. I think my starter pulls 80amps at 12V.
With that amperage...12V 4ft. A 1% voltage drop requires 4awg.
The stock bike is not 4awg. It may be closer to 12awg which is a 6% drop.
Size your wires correctly then add the supercap if you need it.
Your ground wire to the frame should be 4awg as well.
A super capacitor is already a sort of hybrid between capacitor and battery. I would think it much easier to just put in a bigger battery, possibly lithium, if you are going to make room for a super capacitor. Like F64 said, why complicate it.