At the risk of duplication (see this and this), is leaving any reference to a STEM PhD off your résumé considered dishonest? At most I would think of it as "withholding information," but I have the feeling that I'm being filtered out by the HR software.
Is leaving a STEM PhD off your résumé considered dishonest?
No. There is no requirement to include any or all of your degrees on your résumé.
If you do leave it off, make sure the timeframe during which you studied doesn't leave a gap in your background. If it does, be prepared to explain in case it comes up during an interview.
While I have never held it against anyone I was interviewing if they attained higher degrees than called for in the job description, perhaps your situation is different. I know that some folks would be worried that you are over-qualified and would feel bored or underpaid.
And I don't personally know that folks use HR software which would filter out a candidate based on the presence of a STEM PhD. I suppose it's possible, but I've never seen that happen in many years of hiring. If I had to guess, I'd say there's some other explanation for why you aren't generating interest.
Your resume is a part of your story which you tell a potential employer to convince them that you are the best fit for the job. The story should contain true facts and events. But you don't have to include everything. Just as with the PhD, you also don't have to include jobs which didn't work out, or jobs you had to pay bills but don't contribute to the story, or any other personal events which don't contribute with the story you're trying to tell.
Some employers will reject great candidates because the candidate lacks an appropriate bachelor's degree. Other employers will reject PhDs because they feel that the PhD will use this job as a stepping stone to a better job as soon as possible. And you can never tell which employer will do what.
If asked about gaps, just answer honestly. If they press, just state confidently that you felt that the PhD on the resume was getting you screened out of the hiring process. I'll bet that most will feel bad that their screening people or software are filtering out good candidates. Some will be annoyed that you were screened in "unfairly" for leaving your PhD off your resume, but they have no obligation to hire you, so that's their cost of doing business.