Aplying for EAD?

I cannot speak on behalf of your company but since they have gone through all this time and expense I would be very surprised if they would cancel your application, but it does happen.

However yes you may file form I-765 at any time.

Since you are filing the I-765 separately, you will also have to submit a copy of the receipt Form I-797C, Notice of Action (NOA), as evidence of the filing of the I-485. Doing this will exempt you from paying for the cost of filing the I-765.

If you do not have the NOA then you will have to pay the additional cost of filing the I-765 which is $340.

Applicants with a pending Adjustment of Status Application who did not pay a fee that incorporates the cost of an Application for EAD and an Application for Travel Document must continue to file separate interim benefit applications with the appropriate fee for each service.

You appear to be subject to a fee. If you are an L-1 or an H-1B, and you are still employed by the petitioner for either of those classifications, you do not need an EAD card.

One reason you might want an EAD card would be because your petition expires before you become a legal permanent resident. Another reason would be to change employers, but if you change employers, the employer who submitted the I-140 can withdraw it.

If you departed the U.S. and returned as a parolee instead of an L-1 or an H-1B, then you'd want an EAD card, but if you can stay in status as an L-1 or an H-1B, you don't need an EAD card.

Of course you can apply for EAD now. Look for form I-765 on the USCIS website. It will be free for you. It's a very simple form, you will need to fill it out, 2 photos and a copy of I-485 receipt. See form instructions. Mail all papers to the appropriate USCIS service center (see the USCIS website) depending on where you live.