This calculator purports itself to be based on the pure classic formula without fudging in any correction for spoke elongation or rim compression, as many online spoke calculators do. If the numbers input were accurate, here would be my verdict: short by 3mm is in the realm where you may get some threads showing with 12mm nipples and shouldn't do it with aluminum nipples because that's where you really want optimal thread engagement. Best would be go to 16mm brass nipples if you can stand it; they drop the start of the thread down a little and your thread engagement should be pretty good with them.
I will note that calculators of this sort where you choose the parts and trust their dimensions are really a leap of faith, particularly with rim measurements. I'm a firm believer in measuring the rim firsthand and doing it with the nipples you're going to use for that build. A measurement taken this way is what the classic formula expects to have plugged into it.
If you round up to 276, only do so with extreme prejudice against the risk of running out of threaded length once you're nearing final tension, because that can happen and then you will have to either start again or accept a sub-par result.
All the 270-276 lengths are mainstays of the 650b/27.5 era. In case it's unclear, they're all common lengths and a shop not having them suggests either simply being out or being a shop that doesn't really build wheels. If local availability is the challenge, I highly recommend just buying them online by the each or getting the Sapim 20-packs.