1. The letter from your current boss is supposed to be longer than others, describing more details of your work and qualification. Therefore this letter is worth waiting.
2. Never attempt to cheat - you would be cheating your professor and the goverment (BCIS)!!!!, and once found out, your future is done!
3. One way to push your boss is to draft a letter for him/her. It is your business, you have to push, push and push, within a reasonable limit.
Good luck.