H1B grace period over, new Company filed LCA but thinking to withdraw due to long waiting time

My new company filed LCA on 5/8 and my H1B grace period is over on 5/13. They are thinking to withdraw my application as their lawyer suggests that waiting time will be 3 to 5 months and I also need visa stamping. Since US consulate offices in India are closed, I was thinking to go to Mexico either Nogales or Tijuana for stamping, but I cannot see the appointment dates on them. Can anyone suggest what are my possible options?

Also,

  1. Will it take 3-5 months no matter what to get H1B transferred since I have passed my grace time, and no premium till June 29th.

  2. If by luck I get visa transferred, what are my options to get stamping?

Thank you,
Gautam