The problem with a two party system is that if you split your votes, you will lose and the more classical conservatives are not yet willing to lose. The Democrats faced this situation in the 20's-40's. A significant minority of their party was in the South and was pushing Jim Crow laws and discrimination. In the end, they did split with the Dixiecrats rising up and their candidates winning all the Southern elections but losing nationally. The Dixiecrats reluctantly merged back into the Democratic party then shifted to the Republicans in the 70s and 80s and make up the key base for the Republicans today. If classical conservatives want to split from Trump Republicans, they know they are looking at losing elections for several cycles.
Yes, wasn't there some talk among the 'traditional Republicans' recently about breaking away from the Trumpists? And their conclusion, to date, was just as you said.
I don't know what that party can do to heal itself, but if they want to represent mainstream American Republicans, they're going to have to do something. The split seems massive, although the traditionalists are fairly small in number, comparatively speaking.