With Blind Counterbores I have had the best luck coming in with an Indexable Drill that would give you near a flat bottom and then cleaning up with a Necked End Mill to give you the flat bottom counterbore you need. Here are the 2 tools I'd recommend:
Tool 1: Kyocera 1" Diameter 2XD Coolant Thru Indexable Magic Drill
Run at 500 SFM and .0045" IPR. (8.6 IPM)
This is available in a Kit that includes the Drill Body and (10) Insert with 4 Cutting Edges per Insert. This Drill uses the same insert for the inboard and outboard pockets and gives you near a flat bottom (you will want to leave about .030"-.050" at the bottom of the hole for the End Mill to Clean up), here is an image of the drill profile at the bottom of the hole:
Tool 2: 3/8" Diameter x 1/2" LOF x 2-1/8" Neck Length x 4 Flute APLUS Coated Variable Pitch End Mill
This Tool is necked back to give you the clearance you need to come in and clean up bottom of the bore and give you a flat bottom
Run at 300 SFM and .0018" CLPT (3,056 RPM and 22 IPM)
Hopefully this helps!
Mike