The term Allrounder in its purest sense is used to define a player who can make the side on either his batting or bowling alone.
Based on this, a 'Batting Allrounder' should be a player good enough to be selected for the side consistently on the strength of his batting alone, but not with the ball. However, OP has suggested that we are looking for a batting allrounder who could have had a career as a pure bowler as well, albeit a much less successful one. So right off the bat, we can eliminate names like Tony Grieg, Ted Dexter and Wally Hammond. They are all definitely better batsmen than bowlers, but would they, as bowlers alone, have broken into the England side?
Keith Miller and Botham have been mentioned quite a bit, but they should be excluded on two counts:
a) Both were proficient enough with the ball to have made the side on the strength of their bowling alone, and would have had pretty good careers.
b) As good as they were with the bat, would they have been selected consistently based on their batting alone? Probably not.
Then we have guys like Aubrey Faulkner, Vinoo Mankand, WG Grace and Imran Khan. They were all selected on the strength of their bowling at first, but their batting grew to a point where they could be selected on that alone. They evolved as cricketers along their career, and thus they lie somewhere between Bowling Allrounder and Pure Allrounder, depending on what phase of their career your evaluate them on.
Monty Noble and Clive Rice seem to be players who were Pure Allrounders through and through. It's worth wondering if they would have had a successful career on either skill alone. Maybe they would have. Still doesn't fit OP's requirements though.
Procter is an interesting one. What I read was that he was quite a force with the bat; it's just that he was a much better bowler. Often he wouldn't take his batting very seriously. It could be argued he could have made the South Africa side even if he couldn't bowl, and had focused on his batting alone. Then again, I suppose the same argument could be made for Keith Miller. Either way, he is much too good a bowler to fit OP's requirements.
I think the best call for a player that fits OP's requirements is Jayasuriya. After all, he broke into the SL ODI side as a bowler didn't he? I think its safe to say he might have had a few Tests alongside Murali even if he couldn't bat. And his batting was definitely much better than his bowling.