The McMaster Carr listing is for an M2 steel which is a 'high speed steel'. It is formulated for use as cutting tools, where hardness and ability to retain hardness at elevated temperatures are the primary requirements. Strength is secondary, with shear strength and tensile strength (to resist bending or deflection of a cutting tool in use) would be considerations. However, M2 is a comparatively brittle steel.
There are some newer alloy steels that are used for things like industrial/hydaulic wrench parts that have some incredibly high strengths and are 'tough' as well.
Even a steel like a 4340 or 4140, when heat treated properly, will develop some comparatively high strengths. I do not know how high a tensile strength the OP needs, but a heat treated 4340 or 4140 can (if I remember rightly) have an ultimate strength of somewhere around 100,000 psi or a bit more.
The issue with some of the higher strength steels is that the yield point stress value crowds up closer to the ultimate strength value. In plain English, this means the steel has little deflection (within the yield point range, where the steel will return to normal dimensions), and even less ductility (ability to deform or 'stretch' in what is known as 'plastic deformation'). As I like to put it: "There is little warning and then 'SNAP !!"
Stressproof steels are supplied with a hammer forged and cold drawn process. I do not know of any other off-the-shelf alloy steels supplied in bar stock made by hammer forging as opposed to rolling or drawing.
All of this brings back fond memories of my days as a student at Brooklyn Technical HS in the mid 1960's. We had a basic strength of materials course with a well equipped lab. We 'pulled' various specimens of steels and different metals. I remember the wonderment I had as I watched an ASTM 505 (.505" diameter across the test shank area, or 0.400 square inches- handy for calculations in the slide rule days) specimen stretch like taffy before 'rupturing'. We kids had to plot the stress-strain curve and calculate the modulus of elasticity. It was an incredible lesson and something that became a true 'foundation block' not only my education but my life's work as an engineer. I tend to think in simplistic terms, and one thing I fixed in my mind is that higher strength metals are not always the ideal material until I see the spread between their yield point stress and ultimate stress. Tight spread = a material that 'gives little warning and goes 'Snap !"
At the hydroelectric plant I retired from, we were making the switch from slugging wrenches and 16 or 25 lb beaters to hydraulic wrenching systems. I was astounded at the light weight and thin walls on some of the wrench parts, and asked the tech rep about it. He told me they were using titanium for some of the wrench mechanism bodies or frames, and some very high strength alloy steels formulated for the wrench sockets and drive parts. He may have said some of those steels had yield strengths well up over 100 or 150,000 psi. Find some of that steel and the method of heat treating it to get that strength and the OP will likely have all the strength he needs.