Language visa - tourist schengen visa combination

I've searched through the topics here and other forums and couldn't find what I'm looking for. I've found similar situations, and I think my situation is perfectly fine, but I'd like to double (triple, quadruple) check just to be sure I'm not doing anything wrong.

I'm an Aussie who's been in Germany since December, so the end of May will be 6 months for me. The first three months I was here on a tourist visa, and for the next three I got a language visa (since I started learning the language from the beginning anyway). I would like to continue living here and finish B1 (as I feel if I stop now there's no point to the effort up until now).

Now, as my language visa is up at the end of may, I'm wondering if the following scenario is legal and ok:

-End of May I'll have been inside of Schengen for 180 days, 90 days as a tourist and 90 with a language visa. Does that mean I can continue being here for another 90 days as a tourist? This seems perfectly valid to me, but I want to be sure.

[EDIT] The following SE topics are very similar to my situation, but differ in the fact that I've been here for 90 days as a tourist and 90 days with a language visa. The other guys have been here for longer. I am guessing it's the same for all of us, but it's all speculation so far:

Link 1 Link 2 Link 3

[EDIT 2]

I went to the foreigner's office yesterday and was told that:

A) I can continue on with a tourist/schengen visa, but I'd have to fly out of Schengen and fly back. I have no idea why that's a must though. I also can't confirm this is the rule since this was someone who worked at the administration part, not a lawyer or similar. B) Extend my language visa.

[Edit 3]

Combined with what I found on the net, the info from the Foreigner's office and @phoog's reply below, I believe I have my answer.

Cheers