Learn Russian: Ради спасения я должен очутиться около сирены. - For the sake of salvation, I must find myself near the siren.

Очутиться is a defective verb that completely lacks a first-person singular future form. You cannot say я очучусь or я очущусь because those forms do not exist in standard Russian. To talk about yourself, you have to use a workaround, like pairing the infinitive with a modal word such as должен (must) or смогу (will be able to).

If I wanted to state 'I will find myself near the siren' as a simple fact, how could I phrase it since очутиться is defective?

You would swap очутиться for its close synonym оказаться (to turn out / to find oneself). Unlike очутиться, оказаться conjugates perfectly well in the first person, so you could simply say я окажусь около сирены.

Does the verb очутиться imply traveling to the siren intentionally?

Not exactly. Очутиться usually means to suddenly or unexpectedly find yourself somewhere, as if by accident or magic. By pairing it with должен (I must), the speaker makes it sound dramatic or urgent, like saying 'I must somehow miraculously end up near the siren.'

Both ради and около trigger a case change in the words that follow them. Which case is being used as a refresher here?