Currently on a L1B. Need to change employer. What are the ways possible

Hi Currently I am working for an Employer A, who is willing to file for my GC. From what I understand I may be considered under EB2 (or may be EB3) category. I am from India. I am interested in switching the jobs. I have following questions: 1. Is it still possible for me to get an H1B with current H1B cap at 48000 ? One of the employers, is willing to file for a H1B for me by Monday, i.e. 4th June. 2. When is the earliest I can change the employer, if say my GC is filed within a month in EB2 category. Will it be possible within a year ? If not, H1B for next year looks to be the only way.