L1 to H1 through COS but I 94 expiring before Oct 1

I got me H1 approved through COS with start date from October 1 through company B, but my current L1’s I94 through company A(for which I am currently working) expires on September 29.

This being the case, I think I would be out of status for September 30th alone, pls confirm what are my options to handle this without going out of USA

I am in the same situation this year. What did you ended up doing for your Sep 30th 2013 out of status problem?