Depends on the rules... The southern states would be the fastest and easiest. Starting in the east you could just follow US-90 as far as it went and generally head west from there. Your 6-8 month number sounds really high, That sounds more like walking across the country. You could manage it in a couple months without doing super long miles, You wouldn't really need a compass but one would be nice at times.
In any case you could avoid too much back tracking by staying on more major roads than you might otherwise choose. I kind of like roads with the US designation any way so for example US 90 is a good way to go. If you insist on a particular part of the country or really minor roads more backtracking will likely occur. For example, there are very few roads crossing Idaho.
It would actually be pretty fast and easy. The toughest part would be the Sierras, but getting over the mountains is much easier along the southern tier.