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

Zhitaoxun 28 Bolt and Nut Identifier Gauge Nut and Bolt Thread

Thread Data Charts-R-SERIES PIPE THREAD (BRITISH STANDARD PIPE

Basic Thread Concepts

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1/4-28 UNF Close Tolerance NAS Bolts - NAS1304

Tap Size Chart - Machining

Item # DLHT 1/4-28 Set Up, DLHT Double Lever Hand Tool On Sherex

Introduction to Nut and Bolt Sizes

Tap Drill Chart

Thread Pitch Vs. Threads Per Inch (TPI) - Albany County Fasteners