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

Thread Chart (Metric) Major and Minor Diameters

Prime-Line 1/4 in-28 x 3/4 in. Grade 18-8 Stainless Steel Flat

uxcell 1/4-28 UNF Tap and Die Set, HSS Machine Thread Tap with

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

Size Chart – SooBLUBoutique

Grease Fitting Relocation Kit

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 Taper Male x 1/8 NPT Female, 90 Degree Grease Fitting

1/4-28 UNF 2B STI Go/NoGo Thread Plug Gage w/handle-Class X

Everbilt 1/4 in.-28 tpi x 3 in. Zinc-Plated Grade-5 Cap Screw

What size drill bit would I use to drill hole to then to a 1/4

Tap Drill Chart

Thread Chart (UNF-UNC) Major and Minor Diameters

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