B2L2

Read this:  Working While on Claim (WWC) pilot project

http://www.servicecanada.gc.ca/eng/ei/information/wwc.shtml

Do you own calculation and see which way works best for you.  Wish you luck on job hunting.

B2L2

I don't think which employer matters.  It is quite common for previous employer to have left over work.

what's the result after your own calculation?  I think in most case, doing the part-time and then report it back to EI will results in better income.