I'd do the regular 22-250, for the reasons you stated. It'll kill 'em as far away as you can hit 'em.
For a walking gun, I wouldn't even consider a .700-.750 muzzle diameter, that's a number 5 through Rem varmint contour realm. Too much for a walker. I wouldn't go over a Rem magnum profile, which is around .650, and keep it at 24 or under, and get it in an 8" twist.
I just put one together that's similar. 23" Rock 8 twist Rem mag contour, .655" at the muzzle, chambered in 22-250 Ackley, sitting in a McMillan Classic stock, with a Leupold 3.5-10 CDS in Talley rings/bases. Weighs in a 8 1/4 lbs. Add in five rounds, bipod, and sling, and that's all you want in a walking varminter.
you need to shoot my 700 in .223. It's got the generic #5.5 contour that Remington uses, but the barrel length is twenty inches long. I figure I lost about 75fps over the twenty six inch barrel. The shorter barrel is about three times more rigid, and the balance is so good that it's easy to shoot off hand. I'll probably rebarrel that rifle this year if I get the time & money. But the barrel will still be no more than twenty two inches long. In the 22-250 case type, I think the twenty four inch barrel is about right (a 23" would work as well). Honestly that rifle chambered in 6BR with a 22" barrel would be a killer! Or better yet 6BG with a 22" barrel and a 1:10 twist for 87 grain bullets. Now I'm thinking too much
Have yet to shoot a bobcat but if they are anything like ditch panthers a 22-250 or 243 is gonna cuttem in ½!!
My walking varminter is a CZ American in 223= Light & accurate with enough power to putem down without blowing them in ½......Coarse if your into parts
In the 6mm's I used to own, the 80 grain Blitz at about 3400 fps would often cut a coyote in half at 200 yards. In OTW not very fur friendly<g>! None ever get up and run away.
Something that has worked for me has been a 257 Roberts....
Flat shooting good for most hunting needs, to save hides use a nos n/p bullet and to a fragmental bullet the vmax will do the job....
For a walk around rifle a sport barrel would be a idea......
As far as reloading the 223 is about the cheapest and a great selection of bullets.....
The 22-250 Has a lot going for it but the 223 is about 200 fps slower but barrel life with
the 22-250 is about 800-1200 rounds depending......The 223 has 3500-5000 rounds before you
will have to rebarrel the 243 is not far behind the 22-250.......
Choices one do all 257 or 223 a choice........... .02