[Nyororin]

Technically, yes - a trip outside of Japan would allow you to have your 90 day visa renewed.

However, reality might not be so kind to you. All entry to the country is pretty much at the discretion of immigration. If they don`t like that you just popped over to some other country and came back, they are not obligated to let you in. It used to be pretty much guaranteed to work - now I am hearing more and more stories about people being denied the second visa.

I wouldn`t risk it these days.

ETA; You say you are engaged - If you have a wedding planned and proof of this, things will be much smoother.