LTVP+ chances are near zero in the near-term. She was granted a LTVP, and she will be considered for a LTVP+ automatically, at her next renewal. There's no separate upgrade application to LTVP+. In principle ICA could grant her LTVP+ before her next renewal (unilaterally, on ICA's own initiative), but I've never heard of that happening. It wouldn't hurt to ask (at the formalities appointment) whether LTVP+ can be granted, but it won't.
I assume you're aware, but just in case you're not, she'll need to switch from her work pass to an approved Letter of Consent (on her LTVP) in order to continue working. That'll probably require her taking a couple days off, and she should let her employer know they'll need to do that (and coordinate the timing as best as possible).
The pregnancy has no impact on any of this, at least not directly. I assume you're asking about LTVP+ and PR due to the lower medical rates at public hospitals. She can apply for PR now, but you should not have any expectation she would be approved for PR before delivery. But it's not all bad. I think you can still apply Medisave funds (if you have them) to maternity care. Also, your child will be born a Singapore citizen (I assume), so you should get some help with post-natal expenses. I think required immunizations are free, for example (or at least very cheap). Your Singaporean newborn will also receive an automatic $4,000 Medisave grant upon registration of birth. You might want to take a look at signing up your whole (growing) family for an Integrated Shield Plan (the lower cost public hospital type), although watch out for pregnancy exclusions and be aware of those.
Right now, for reference, NUH has the lowest total bill sizes for an uncomplicated, normal (non-Caesarian) delivery in the 4-bed B1 ward. KKH has a 5-bed B2+ ward which might be slightly less expensive (ask, but when you ask make sure they know that your wife is a LTVP holder). B2 and C wards (6 beds) are not air conditioned. You can also ask about rates there, but again you should make clear your wife is a LTVP holder to get the right rate information.
Good pre-natal care is really important to help avoid unexpected medical expenses. Try not to cut back on that, even if you have to pay a few more dollars for an "extra" checkup. Let your doctor know that your budget is limited, but try to stick to your doctor's advice.