Strategy for moving to Japan - 31/M - qualify for HSP visa

Essentially title.

I'm a 31/M network engineering and cybersecurity consultant here in the US, highly certified, and have worked for some very large global organizations. My Japanese level is probably around a ギリギリ N3 pass. I've been studying in earnest for around 10 months.

I do have 11 years of experience in my industry and as long as salary is right I'd meet the 70 point requirement for HSP visa even without a degree or N2+.

The problem I'm having is finding a visa sponsor. I guess I'm just looking for advice and guidance on how to actually land a job in Japan while being here in the US. I've had an interview and referral to a large US-based cyber security company but they essentially told me that "We love you, but we can't sponsor your visa, call us again when you find a way to get into the country"

I've met with a Japan market entry strategist, created a Japanese LinkedIn profile, have Japanese and Bi-lingual resumes, etc. I'm just not really having luck other than a single interview with Rakuten, but did not get the job due to lack of cloud experience.

I'd like to immigrate to Japan as I'm simply not happy here and have a lot of friends over in Japan.
I plan to sit for N3 in December, my current plan is to come over on a student visa and go to language school for 2 years while I network and try to find a job. Is this my most realistic route? Is my current US salary scaring Japanese HR departments, thinking I'll scoff at what they can offer?

Even without N2+ Japanese. I would think I would at least be getting some bites with my experience, achievements, and technical credentials.