It is critical on a bridge, that nothing weakens the main load bearing cables, especially as they are strained to give as flat a bridge base as possible,
I have seen a few rope bridges with wooden walkways and they were all slung as a slack line ie a gentle downward curve not a taut flat surface. But maybe I've been looking at the wrong bridges.
I would be surprised if the support cable were steel as thick as described in the original post - I don't think that this is for driving a vehicle across!
Barry
Interesting then that the very first picture in the very first reference link is this-

Of course, a flat bridge like this is only possible because the bed is suspended on the heavily curved suspension cables.
I agree that a normal bed suspended rope bridge as the OP is proposing would be gently curved, but it would be exactly that-'gently curved', because a steep curve turns into a ladder and the planks become impossible to grip in wet weather. Much more slope than ca 1 in 5 becomes hard work, and a 1 in 5 'flat' amplifies the load of bridge + passengers by a factor of 500%.
Granted, the OP has sized the load cables at 2" which presumably have a massive safety margin, but the flatter he tries to get the bed, the greater tension he will create in them when a passenger(or three) adds to the weight of the bridge.
@Lindsey
I did not mean abrasion, but U bolts tightened so that they bite into the wood are well capable of delivering such a mighty nip that they will significantly weaken the suspension cable.
As a generality, the less elastic a cord is, the more susceptible it is to compression failure, and high modulus rope is rarely used as a bridge bed - who wants a 'bouncy' bridge?
The nip/compression effect I am referring to can be demonstrated by simply gently pinching a strand of cooked spaghetti between finger and thumb. A more dramatic example can be seen by pinching a large soft eraser across its middle, eventually, the centre of the eraser will split under the internal tension created by the nip and the eraser will break in two - In England we have candies called 'Jelly Babies' that demonstrate this effect very easily.
On a load critical construction, forces should be transferred by contact friction i.e. multiple round turns, not by high point pressure nip type connections, so for this application I would use round turns...
Bring the descender cords down from the rand rail cable , feed through one hole in a plank, wrap half a dozen times around the suspension cable and feed back up through another plank hole back to the hand rail cable. The round turns will provide the necessary grip of the main cable to keep the planks in place and will also act as an abrasion buffer between planks and main cable. Checking for wear would simply be a matter of lifting a plank up and sliding it a few inches up the side cables to inspect the turns.
For me, the greater challenge is how to attach the side cords to the hand rail so that you have adjustment to allow all the cords to be given the same tension ( you don't want 'baggy' cords), and at the same time ensure that the will not slip/slide along the hand rail cord when passengers run their hands along the hand rail for support in transit. I do not at the moment have a solution for this one... a lockable/unlockable, adjustable, gripping hitch?
Derek