Who is going to appeal to them most?
Reagan won independent voters in droves. The independent voters went for the republican party in 2010 in droves.
The answer is not to be a mushy moderate. Stand for something, lead and people will follow. Even the mind-numbed independents. This has always been true.
Pandering and being all things to all people leads to close elections that democrats can steal. Standing up, being unwavering in your principles leads to overwhelming landslides.