I don't think I'd be all that excited to build a .300 Ham'r on a short action 700 or uni-sized T3 action. I'm not sure what the advantage would be going with an action that will easily accommodate a larger, more versatile cartridge like the .308 Win.
If I were building a bolt action .300 Ham'r, I'd want an action that's more svelt, like your CZ 527.
If being a lefty wasn't a requirement, I think a Howa Mini would do well.
Not one of the Kool Kid's, but...
Agree with Dan... At least in theory, as I've got a 300 Blackout and a 221 Fireball on Rem. Model 7 actions, and the action size bothers me not at all.
I've had a CZ 527, nice rifle & loved the set trigger, but I'm not a fan of extended magazines.
The Howa Mini would be my choice... Not avail. left handed? That sucks.
I've always wondered about the twist Wilson uses on the Hammer (1:15). Surprises me that it stabilizes 150's at Hammer velocities.
I'd go with an 18" barrel for suppressed, just to keep the length reasonable. For a handier "Ranch" Rifle I'd even consider 16.5".
For bullets Speer makes a bonded 150 for Blackout velocities (2,100 - 2,200 fps). Good luck finding any, if you do PM me a link.
Once your 300 Ham'r is a sure thing, if interested, PM me and I'll send you a few Speer 130 FN Game (not varmint) bullets so you can see if they feed OK.