It's not so much about the frame as the position and your specific condition.
As you point out raising the bars is likely to help, but it's a question of how much is necessary.
Depending on your height and frame size there's a good chance that a sloping top tube frame might bring the starting place for bar height higher. But there's no assurance, so you'll need to measure a bunch or frames to find the highest head height. Then you might get enough from a high angle stem and drop bars. You might also tinker with a shorter reach and the levers moved up, to stretch your spine out a bit less.
All this will probably not help if you need more than small improvements. If so, a straight bar and shorter stem, in the style of trendy fixies might be the answer.
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