If your current company has an approved blanket L petition it seems that you could possibly change status while in the US (see USCIS.gov excerpt below). What I'm not sure of is whether change of status to L1 = abandoning AoS. But it makes sense that it would be abandoned, because you're no longer on the B2 or expired B2, you're on an L1 and would probably need to apply again to adjust from the L1 instead.
If you have the offer, it doesn't hurt to try and expedite your EAD based on financial loss. This may have changed during Covid times, but there are expedite cases on here that are four weeks from application to EAD in hand.
(from USCIS.gov:)
Change of Status Request for Beneficiaries Who are in the United States:
All petitioners requesting a change of status to L-1 based on an approved blanket L petition for a beneficiary who is currently in the United States must file the following:
Form I-129, Petition for a Nonimmigrant Worker, and
Form I-129S, Nonimmigrant Petition Based on Blanket L Petition (the 06/02/16 edition only).
We may reject any Form I-129 for an L-1 blanket change of status request that does not also include Form I-129S.