The cardboard is definitely oxidation as mentioned before and most likely has nothing to do with whether you did an AG or extract and nothing to do with your temperature not getting down low enough (not that hat is not an issue - it just isn't related to the cardboard).
There is some great advice given above and it will all help you make better beer, but first focus on everything that is related to solving this oxidation issue before moving on. Do it step by step and look at every possible point where oxidation can come in. Is the transfer from the fermenter to the bucket smooth (the hose is all the way to the bottom of the bucket and the connection from the hose to the raking cane is firm and clamped if needed)? I am also confused by this statement you made:
Too slow should not bring oxygen into the flow. If you bottle from the spigot and have a good seal of the hose to the spigot, there is no oxygen in the path of the beer to the bottle - it is a sealed system. If you see bubbles, it is either residual CO2 from the beer breaking out of solution or a bad connection of the hose to the spigot. Too fast is not introducing oxygen either. If the flow is so fast that it is causing a head to form, that head is made of CO2 from solution, not O2. Two solutions to too fast - the speed is related to the change in elevation between the beer inside the beer bottle and the level in the bottling bucket. If you have a 4 foot drop, you will have fast flow regardless the diameter of your wand. At the beginning with a full bucket, you can actually start with the bottom of the beer bottle and the bottom of the bucket at the same level. Second, keep the wand (which I assume has a spring loaded valve at the bottom) firmly against the bottom until the bottle is full and overflows beer, not just foam that might be caused by fast flow. The space made by removing the wand at this point creates the correct amount of headspace. Why fill until the instant it overflows? Unless you purge all of your bottles with CO2 before you start, they all have O2 in them. Filling all the way to the top past the point where foam is coming out and just to the point beer is just spilling out ensures there is no oxygen left. Yes, when you pull you the wand, its displacement now draws a bit of oxygen back in, but leaving caps on loose for a bit before crimping them on lets some of the CO2 in solution break out and push out the O2 plus you have O2 reducing caps to clean up the rest. Last point - since the bottles will have a bit of O2 from the displaced wand, move them gently once filled so as not to shake them up and mix that O2 in. Once the O2 absorbing caps are on for a while and have time to work, you don't need to be as careful.