You seem to think that it's virtually impossible to get over the Rapidan. And yet it was done repeatedly. I believe Meade was the last one to do it, during the Mine Run campaign, before Grant came east.You can't just dismiss a reason by calling it an excuse.
It's fact that getting over the Rapidan by the Overland route involves three options and none of them are good; if you are willing to argue that an Overland campaign in 1862 was militarily plausible (in the face of the opinions of not just McClellan but every divisional commander of the Army of the Potomac in March 1862) then you need to either accept the problems and admit you do not have a solution to them, or provide a solution.
There is no reason to believe a '62 Overland campaign was impossible.