Regarding your EPHi,
For your EP, you need to have your current employer cancel your EP with MOM. After that, the bank can file an application with MOM again. You get a white card after cancelling your EP which grants you 1 month stay in Singapore.
I am in a very similar situation with you. if you dont mind, can pm me your email address? Thanks.
No need to cancel the current EP if you want to change employer
I checked the MOM website:
To apply for a new Employment Pass whenever the Employment Pass holder changes an employer. There is no need to cancel the existing pass before doing so.
Please refer to:
http://www.mom.gov.sg/foreign-manpower/passes-visas/employment-pass/inform-mom/Pages/update-of-details.aspx#employerchange
I visited the MOM in person on Mar-07-2011,got the same answer.