I would use a half inch endmill for a pocket that deep, and as short as possible, long length small diameter equals chatter, thats a fact.

Carbide cutters are stiffer than HSS ones, that may help also.

I only use long length cutters for wood or plastic mainly, and always try to use the largest diameter and the shortest cutter possible for a given job in aluminum or steel, as chatter ruins the finish. Also take a light finish cut when done.

When I make a part I dont want to hear any chatter, if I do I adjust the settings or adjust cutter length to where it goes away. I sharpen most of my own cutters and that will give you first hand knowledge as to how shorter longer cutters react to chatter.

Also going too slow on the feedrate will cause the cutter to rub and thats not good either.

It all amounts to getting a "feel" for machining, what works and what doesnt etc.

I also dont like to push machining limits, but then I dont do it for production either.

I hope you get it figured out, good luck on your project.