The L1 can be worse than the H1 bind in some ways - has effectively all of the same rules, with the primary and critical exception you cannot change employer in the US. On the L1, your Green Card is much more at the mercy of how nice your employer is, as you won't be able to change job if they start slow-walking it etc. The trade off is not being subject to the H1 cap of course.

You can also try to convince your employer to keep applying for an H1 for you while you are working on an L1 - if they agree that's usually a good sign the employer is going to work hard to complete your GC process, and isn't just using the L1 status to handcuff you to the company.