I used to run parts for an electrical contracting company back in college. What you need is a Mouse! It's a trick for pulling wire through long runs. They use a foam plug attached to a nylon string and blow it through with a CO2 tank that has a rubber plug with a hole for the string on the end of the hose.
I did my wires this way, just get some nylon string, shove it in the hole and blow it through with an air gun. You won't believe how fast you can get that string from one point to another.
Next, get a few of the wires together and lay about 4" of the string along side end to end and tape together with electrical tape. Then take the rest of the wires and tape them to the first batch a little farther down so that you end up going from string to 3 wires to 6 wires, etc.. Then pull them through, if you don't want to use grease a simple wet bar of soap will work just fine to lube them up without a oily mess.
Another thing I did on my frame was to drill a 1/4" hole near the bend. There are some sharp corners inside that frame that can strip the wires. If you drill the 1/4" hole and shove a bolt or phillips screwdriver in the hole, the wires will pull against the rounded shaft rather than the sharp corner of the frame and keep them from getting damaged. Once you're done, put a plug or grommet in the hole to cover it up.