.223 for bear, mountain goat, deer, elk, and moose.

I didn't read through all 677 pages of material here so forgive me for searching for a quick answer. My son has a Ruger American Gen2 .223 with a 1 in 8 twist. I have been doing some load work-up for it using varget and 77gr TMK's. Question for this group, what velocity should I expect this to get to with a 20" barrel once I work up to a near-max safe load? I'm limited to 2.260" OAL seating depth.

Also, varget is just what I have on hand. Has there been a different powder that has had consistent results for most people that are using the 77's?
My boy has the same rifle and with 24 gr of Tac at 2.260” with a fed 205 primer in LC brass, he’s getting 2,744.6 fps. It shoots great for him.
 
They all look awfully dead. What size beasts are we looking at here? I'm assuming those are 75 to 200 pounds or so. ??
 
They all look awfully dead. What size beasts are we looking at here? I'm assuming those are 75 to 200 pounds or so. ??

Red Hinds(female) from an area renowned for large deer. 180 - 250 pounds sort of thing live except the one yearling which was probably 140 pounds. They are a slightly smaller version of elk for the closest comparison. Most other areas they would typically be maybe 20-30 pounds lighter in general.
 
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