If one pole is rotated toward the Sun, the other will, perforce, be rotated away -- meaning its share of solar energy will be reduced, in extreme cases to zero. There will still be gradations on the globe between arctic and tropical, and with a greater axial tilt every latitude will experience varying extremes in temperature greater than experienced today.
You can't achieve your desired "mild climate" everywhere on a globe.
There may be other factors besides the orientation of the earth's axis, for example atmospheric conditions that facilitated a wider, more even dispersement of heat and humidity. IMO, the general geological makeup of this planet prior to the flood could easily have been far different that what has been observed since. The biblical text makes clear this event had not happened before and would never be repeated. For that reason it does not seem unreasonable to speculate that a vastly different physical earth preceded the flood.