H1b PERM process

[UmaG]

Hi, I am on my 5th year of my H1b and I will be completing my 6th years in 2020 April 31. My current company is not stable to start my PERM process. I tried to switch my job. Many big companies are not willing to hire me because there is not enough time left in my H1b to start my PERM process is what they told. So, I am joining a consultancy for a Contract position with a big retailer client. My Visa transfer is in progress. This consultancy has done one PERM in the past. Is it safe for me to start my PERM with this consultancy or should I file with some other company? What are my other options to make my case stronger?

1. Can I hire an immigration lawyer to review my case documents before this new employer files my PERM?
2. How to find if there are other companies interested in taking my PERM?
3. I feel I am running out of time to start my PERM. What is the maximum time I have to start my PERM?
4. Can someone suggest me good immigration attorneys to discuss my case?