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

24043, Recoil Thread Repair Insert, 1/4-28 UNF, Drill Size 6.7mm

Everything you wanted to know about taps but were afraid to ask

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

Everbilt's Grade 5 cap screws are recommended for medium-duty bolting applications. The grade 5 bolt is compatible with grade 5 and grade 8 mating

1/4 in.-28 TPI x 2-1/4 in. Zinc-Plated Grade 5 Fine Thread Hex Bolt

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

Size Chart - Unisex Quarter Zip – Jupmode

Size Chart Pop Up – Nothing Fits But

UNF 1/4 28G thread, Determination – Thread Types

UNF 1/4 28G thread, Determination – Thread Types

28UN - 60 Degree Unified Thread Dimensions & Specifications

Nut & Bolt Thread Checker (Complete SAE/Inch and Metric Set) - 26