We've developed a technique you might consider. We plant our tulips in
sturdy mesh basket/buckets that we get from water garden suppliers. They
are made to hold pond plants. After the tulips bloom we move them to the
"nursery" part of our gatden to complete their cycle. this allows us to
move plants, roots and all. You'll loose some roots, but its not a big
deal, the plants seem to do fine. These buckets are probably smaller
than you are now using, but they serve us very well.