There are two ways to approach this.
1. Yes the 30-06 in a Win. Fwt. does have noticeable recoil.
I haven't read if you are a handloader or not. I'm assuming, not. You can begin with dry firing drills to build confidence on sight alignment thru the scope and trigger control. After that shows good improvement, at the range, perform the live chamber/dummy chamber drill with MANAGED RECOIL LOADS. Still maintaining sight/scope alignment and trigger control. No anticipation of the shot!
If you ARE a handloader or have access to a reliable buddy, you can do the same with reduced loads and cheap 150gr bullets.
Than work up as improvement is shown.
Also get a PAST recoil reducer to wear.
Don't overlook the .22 rifle as a good starting point to build your confidence.
2. The more spendy solution is to do the same thing only with a lesser caliber, such as a .243.
By the way, I believe there still is merit in a .270Win.. You can buy reduced recoil loads or handload them. The .270Win is a 130gr does have less recoil than a 180gr in a 30-06. If you can rid yourself of the flinches with light loads from a .270Win., I believe you will have a nice two gun combo with it and the '06. Or, you may come to conclude that the '06 and its recoil really isn't needed once the .270Win is mastered.
Good luck.
