I developed a flinch when I used to shoot my .300WM Sendero. Like you said it didn't kick that bad, was more of a shove than a smack. I couldn't shake it so I traded the rifle for a .243 Rem 700 Varmint Special. Shoothing that "little" rifle seemed to settle my mind and me down. I'm back shooting the .300 again. Different rifle altoghther and hasn't bothered me at all. This rifle (112BVSS) has a laminated stock, it's a single shot (no magazine/bottom metal) and feels beefier than the HS Precision stocked Sendero.
There's still more recoil than a .243 but I guess my mind has convinced my muscles it's OK to relax. Wow, that's weird. I was out yesterday shooting a different .243 and .300. I shot them both at 300yds and again at 550yds.
The .243/w 75gn Hornady HP's and the .300/w 180gn SMK's. I shot a 3.641" group at 300 with the .300WM(not so great) and a 4.7155" at 550yds. That wasn't too bad and would have been better if I had paid more attention to the slight (4mph) wind. I have definately gotten tighter groups with the Nosler Ballistic Tips.
The .243 (Win70 HVB) shot a 1.457" at 300yds but at 550yd I only got on paper 2 outta 3 shots. Those two bullets were only 1.5" apart. I know, I know, two shot groups don't count!
Not sure what happened, but I remember one of those three sounding a bit "squibbish". Not exactly sure but I think it landed vertically in-line with the center but about 6-7" low. All loads were dispensed/weighed on my RCBS ChargeMaster. Who knows.
Anyway, you might want to try shooting a lighter recoiling rifle until your mind settles. Works for me. JohnnyK.