My thoughts were to add a couple strips of bar stock on either side to keep them straight, but low enough that by lifting on the spring you could lift over them and swing them out of position inside the bucket when not in use.
It may be a bit before I get this done though, gonna be fixing the front hub tomorrow and back at the woodcutting I missed this week due to it. I promise to get pics when it gets done, though.
BTW, my bucket is wider than most of the compacts on here, 7.5', so mine will be added nearer the center, and cut just long enough that they will fold in without hitting the center brace. Old pic attached with a pretty good view of my bucket. The reason for taking this pic originally was to get an idea how much wood came out of a 24" or so oak round after splitting.