Well, it seems that you have already decided how you want to proceed but I would make a few points:
1. A negative equity mortgage is not subject to the new Central Bank restrictions so you would not require a 20% deposit.
2. You will be in negative equity on an aggregate basis in any event. Splitting you loans in two won't change this reality.
3. You really need to understand the taxation of rental profits before you decide that your apartment is a great investment. It's actually extremely inefficient from a tax perspective, in addition to being a highly concentrated, illiquid, high-risk investment.
Professionally I know of at least a dozen couples that have made exactly the same decision as you are contemplating. Without exception, they all subsequently realised that it was the worst financial decision they ever made. Maybe it will work out for you but, in my opinion, you are taking on an unnecessary degree of risk in your circumstances.