Who do I believe when my agent's ARV is 40k over mine?

Pull the sold comps she used and separate two things: the sale price and the days on market. A comp that sold in 9 days at 315k and a comp that sold in 84 days after two price cuts at 315k are telling you different things about whether 315k is the market or the ceiling. Your instinct that houses at your finish level sit is a days-on-market observation, and it's testable.

Then attack the adjustments individually. Ask her what dollar figure she assigned to the finished basement and to the kitchen, and ask her to show you a matched pair: two sales in the same submarket that differ mainly in that one feature. If the pair supports a 22k basement adjustment, she's right and your 275k is too low. If she can't produce the pair, the adjustment is a judgment call and you're allowed to discount it. Appraisers do exactly this and they're often thin on support too.

The number you didn't put in the post is the resale timeline. 178k purchase plus 62k rehab is 240k before closing costs both ways, holding, and financing. At 315k with 6 percent selling costs you net around 296k. At 275k you net around 258k. That spread is your entire margin, so the question is really how much cushion you need for the ARV to be wrong by 20k, which it can be even with good comps.

One thing that will move this more than the argument: get a licensed appraiser to do a subject-to-completion appraisal against your scope of work. It costs a few hundred and it's a third party with no commission attached. If your lender is already requiring one, ask when it lands relative to your inspection deadline, because finding out after the contingency expires is the version of this that hurts.