I would invest in a dressage whip. It is easier to carry with your reins still in their normal position and still be effective. If your main issue is about him backing up, being able to give that extra bit of "I said forward" from his hind end will help more than a short crop which either requires you to reach back or to pop him on the shoulder.
I do agree with Sky that your transitions sound more like a balance issue than an obedience one. Perhaps some lounging in side reins adjusted for a long and low frame would help him to learn self carriage so he can give you better transitions.