“Tweet Create 300 successful requests per 3-hour window per user” is much too restrictive limit.

I want to post a tweet about every second, if not more often, 24 hours/day 7d/week. (Yes, I have what to post.)

Is there any way to increase rate limits for my account? Maybe, some paid package?

No. Each account is subject to overall limits: Understanding Twitter limits | Twitter Help and posting from the API are the limits documented there. Also, since the limit is applied for an account, using multiple apps won’t give you more - your account is limited itself.