Hi guys, I need some guidance again

I have received EPEC and was planing to get a LTSVP, got even my an "approved in principle" decision by e-mail. But they require a medical exam, and when I called a random clinic about it, they kept repeating like zombies "need letter from MoM". I just have a really general e-mail, and guess that's not the "letter".
On the other side, my husband signed his work contract today, and applied for a Dependency Pass for me.
Now my dilemma: should I push the LTSVP and do the whole medical exam thing (which I am not really sure how to do), or wait for the DP? My approval in principal expires next Monday

And MoM claims, that approval of DP can take up to 5 weeks

Will I be able to stay in Singapore till they make up their minds, or does it actually take less time?
What to do dear expats?
