I think the average marching distance would be around 15 to 30 miles per day
This is enormously too far to be realistic. Typical marching distances were on the order of 8-12 miles per day average for extended periods, though individual forced marches could be further. (Usually a long forced march would be followed by a rest period.)
The reasons for this are many, but one of them is that armies are accompanied by horse transport (for the artillery, ammunition and food, plus medical supplies etc.) and those are the limiting factor - and if you push horses too hard they die. They can go faster over good roads and in dry conditions, and obviously slow down on bad roads or in the wet.
To illustrate what I mean, let's have a quick look at two examples which are usually highlighted as "fast marching" - Jackson in the Valley, and Sherman in Georgia.
Case 1: Jackson in the Valley.
An example of Jackson's fast marching was from Charles Town (marched out May 30) to Harrisonburg (June 6). This was along the good road of the Valley Pike, and was about 92 miles in eight marches (30,31,1,2,3,4,5,6). That's between 11-12 miles per day on average.
Case 2: Sherman's March.
Sherman's March was between 250 and 300 miles, and he marched out on November 15 and camped outside Savannah around December 10. Marching November 15 and camping on December 14 would be 30 marches, so it looks like Sherman's March was about 10 miles per day again.
I'm of course aware that armies in other periods marched further, such as Wellington's army in the Peninsula or for that matter the Romans. But they used different supply systems (bullock carts, mules and often the men themselves, who were long-service regulars rather than short-service volunteers as in America).