To establish residence in Germany, the general rule is that you must first obtain a long-stay German visa from your current place of residence. Then, after entering Germany you would apply for the corresponding residence permit (Aufenthaltserlaubnis).
There are some exceptions but usually it is not allowed to enter Germany on a short-stay Schengen visa (which is presumably the kind of visa you currently have) and apply directly for a residence permit. The local authorities will want to check your visa before entertaining your application for the residence permit (some of them mention this explicitely in their requirements). So using your current visa and going to the Ausländerbehörde is not the right approach.
The requirements for all residence permits are defined in the Aufenthaltsgesetz. There are many different categories of residence permits, all with slightly different requirements. In turn, long-stay visas are governed by § 6 of the same statute:
Für längerfristige Aufenthalte ist ein Visum für das Bundesgebiet (nationales Visum) erforderlich, das vor der Einreise erteilt wird. Die Erteilung richtet sich nach den für die Aufenthaltserlaubnis […] geltenden Vorschriften. […]
In other words for each residence permit defined by the law, it's in principle possible to apply for a visa based on the same requirements. Most of the documentation you find online is from local authorities and provinces in Germany and deals with residence permits, which is why it sounds like it can only be obtained locally. By contrast, the visa must be obtained from a German representation abroad.
A jobseekers visa (§ 20 Arbeitsplatzsuche für Fachkräfte) does not seem like a good fit because, unless I am mistaken, Arbeitsplatz strictly means employment. If you are not looking for a bona fide work contract, you do not qualify. As you note, the EU Blue card is similar and not a good option for you.
I am not very familiar with it but it does seem that residence under § 21 Selbständige Tätigkeit would fit best in your situation. The requirements are quite extensive (business plan, financial means, insurance) and require some familiarity with German business law (registration in the commercial register, etc.) which is why I guess most applicants already live in Germany and transition from another residence permit (including student residence permits).
I did however find a form to apply for a visa for that purpose from the German embassy in Mexico. The best course of action is probably to contact the local German embassy to get the relevant form and requirements for an application.