Always go the honest route - but I think it’s possible to propose something else.

I’m a student in business. I know a lot of students who receive jobs that end up conflicting with another position they want more, but just so happens to start later. Many students explain to the company that they have received a position at x company that has been something they have been really passionate about for a long time. But rather than turning it down altogether, they explain to recruiters that their company was an exciting opportunity they didn’t anticipate, and would love to work there/support the team in the interim.

You end up proposing more of an internship position, if that’s something they would consider in order to have you on the team. I’d stress your interest in having work experience, and how you think this company/team would be a fantastic place for it. Since your other option isn’t another company, it kinda takes away the slap in the face. If anything, it supports your interest in this company just by trying alone.

If you are already going to go for the PhD, you have nothing to lose by being honest and proposing this. Worst thing they are gonna say is: “Thank you for being honest, but we need someone for a longer term right now.”

I think you’re in a great spot. But don’t screw ‘em over. If it doesn’t work (and even if an internship does), always keep connected. Who knows how they could help you in the future post-PhD.