-Most likely your H1 transfer will be approved without the I-94 card. If so, you just need to go outside of U.S. to get an H1 visa to come back to activate your H1 status. If you are lucky, you may get it approved with the I-94. You may just provide the old paycheck stubs and ask your old employer to give you a letter indicating you were on the leave without pay for the recent several months.
Use premium processing to do the H1 transfer so that you can get the result in 15 days.