How to work for New Employer (L1 to H1)

[MrsB]

Situation:
I came to USA on L1B Visa on Sep 2012 through company A.
Company B applied for H1B in 2015 through the lottery process and I got approved i797-A for myself and family valid until Aug 2018.
Company A filed L1 extension in Sep 2015 and that also got approved and continued working through Company A and didn't join Company B on H1B.
In 2016, I went to India and re-entered with L1B Stamping and it is valid until Aug ends 2017.

Now I have got a good Offer from Company C, who is ready to make me on board but stuck with Visa constraints with no premium processing.

Problem:
Since I have not worked for Employee B who filed my H1 and then my L1 extension was approved and I worked on L1, so my status changed to L1. Also last year I re-entered to USA, my i-94 got changed.

Since Premium Processing is not available, Transfer process would take time and whether I can work only on Approval and not on Receipt, please correct.
Is it possible to expedite the process by any means?

Can employer B who filed my H1 and can I work for them immediately, if they file an amendment with new LCA based on last approved i-797A copy?
Is there a way, I can work for either of the options?

Any suggestion would be highly appreciated if I am legally able to work for them before my term ends in USA by next month.
Based on the workable solution, Hiring Manager is planning to make a decision in few days.
 

[JoeF]

Since you are not in H1 status, you would have to wait for the approval. Working on receipt is only possible if you are in H1 status.

Further, since you never worked on the H1, company B was required by law to inform USCIS that you didn't work there. That also likely means that you are not considered counted in the quota, so the H1 petition from company C is likely going to get denied.

An H1 "just in case" is no longer possible.