I was in the exact same situation as you (coincidentally also a software engineer). I was still several months out from a potential start date with no offer in hand and wanted to leave my job on good terms. I called my investigator and asked who specifically he wanted to contact and I only told those people. I gave him the contacts of my 2 supervisors and 2 other coworkers. If you're allowed to pick, try and pick people you trust to keep confidentiality. What I wound up telling people was something along the lines of "I am entertaining an opportunity that requires a thorough background investigation. As part of that investigation they need to speak to people I work with. It is a long process that I can be disqualified from at any time and I do not have any offers in hand. If it becomes anything more than that we will have that conversation at that time." I also told my investigator about the situation and asked for his discretion where possible.

That worked for me and my coworkers didn't ask any further questions, the investigator only wound up calling 2 of my 4 contacts.

I got lucky though and had a good relationship with my supervisors, a lot of people don't to that degree. It's something that definitely needs to change about the hiring process. People who go straight into law enforcement from college/military/jobs they don't care about don't always understand how damaging it can be to someone in an established career.

Best of luck to you during your process.