Saw some post about insurance a few pages back, malas to quote... here is my experience and so far is adequate for me at the moment.
1. Local MY insurance (some can be claimed in SG - via conversion RM-SGD for hospitalization) - ask you agent
2. My insurance policy can cover SG as well with an extra premium - again ask your agent
What I am currently doing (non PR without and Medi save shield thingy).
1. My local insurance policy (life, medical, etc..), I didn't pay the extra premium for SG. So for my policy to be in effect, I cannot exceed 3 months away from Malaysia. If you go back every so often, this should not be an issue and you can continue with your policy OR add more coverage from your earned SGD
2. I bought travel insurance - also the condition of not more than 3 months away from Malaysia as well.
My first policy basically is my investment,life, medical,etc policy (usual vanilla policy) I bought around 9+ years ago, which I still continue to pay the premium. I didn't load the SG part since I go back once in a couple of month, or if needed just go to JB

(keep the ticket as proof, etc).
The second, travel insurance, which can be used to claim for GP, lost luggage, flight delay, etc in the foreign country. Mine cost around RM 400+ a year [renew yearly] (covers almost all countries except Nepal, and some other war torn countries which you will never go). With this I do not need to even buy the insurance being shoved down by airline companies

As usual ask your agent what is covered, tnc.
So basically if there is hospitalization, etc, I will use the company insurance first, if that exceeds, go onto the travel insurance and lastly the personal MY insurance. If you still survive after killing off 2 insurance limit, I think you can manage to cross the causeway to JB to claim your local insurance hospitalization
*There is a max medical (GP claim) per claim in the place I work in, I managed to exceed once, so the extra I claim over on the travel insurance.