On H1B, got terminated with notice period

[Travel worker]

I am working on H1B for last 10 years (H1 extended thru approved 140 petition). I have valid H1B stamped till Jun 2018. My employer terminated me due to budget cuts and gave a notice period for 2 months. Employer will continue to run me in payroll for 2 months for me to find another employer for H1B transfer. After 2 months, they will notify USCIS. Then I believe I have 60 more days (grace period) to find another employer.  Its been 2 weeks and my job search is not going well. 

Should I continue thru my 60 day grace period searching for a job or file H4 with my spouse's approved 140 to be on the safer side? Will applying for H4 affect my H1 status? What is the best course of action?

Please help me with your knowledge in this.