What Is The Next Size Up From 1/4-28?

I buggered up the threads on the forward screw hole on my Remington 700 receiver to the point I think I need to drill it to a larger size and retap. I am thinking of going to 5/16-24 or 5/16-32. Is there a better option? Maybe metric? Hunting season so three weeks away

CSA-80 - Raf Electronic Hardware - Bolt, Spring Anchor, Stainless

37086117,,1/4-28 HELICOIL PLUG TAP Drill 17/64,Jugenheimer

Size Chart Pop Up – Nothing Fits But

Basic Thread Concepts

HELI-COIL, 1/4-28 Thread Size, 1 1/8 in Thread Lg, Screw Thread

1/4-28 x 3/4 Button Head Socket Cap Screws, Allen Socket Drive

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1/4-28 x 1 inch UNF Cap Head Screws (ANSI B18.3) - A2 Stainless

1/4-28 UNF Fine Thread Stainless Steel Allen Hex Socket Head Cap