Immigration visa denial

Hello everyone, I’m looking for some respectful insight regarding my current visa situation. In February 2025, I was granted a 'withdrawal of admission' under Section 212 (a) (7) (A) (i) (I) due to working remotely while on a visitor status. My FOIA records show a discrepancy claiming I was living in the U.S. during a period when my travel history clearly shows multiple exits and entries. Since then, I have had two 214(b) denials—one for a B1/B2 and recently one for a J-1 Teacher Exchange program with Dallas ISD.
Despite having a legitimate job offer and being told I don't have a formal ban, I am struggling to overcome the previous incident. I would appreciate any advice on whether I should continue attempting the J-1 path at a different embassy, or if pursuing an H-1B (dual intent) might be a more successful route given my history. If you have experience with FOIA inconsistencies or teacher visas, I would value your thoughts. Please share only respectful comments; thank you for your time