Based on our conversation, I would say that "my" conservatism would be your classic liberalism tempered by reason and the good of society.
I understand that "reason" and "good" are a nebulous concepts, but it's the best I can do.
I would respond that too often, 'tempered by reason' translates to the imposition of some reductionist scheme on human society.
And the 'good of society' too often translates into the politico-economic good of a power-holding faction.
IMO, classical liberalism has been 'tempered by reason'; indeed, it was the application of reason to the study of history that led to the creation of 'classical liberalism' through the 17th, 18th, and 19th Centuries. And it has certainly been for the 'good of society' that America enjoyed such governance for the first 150 years of the Republic - we are still living off that political moral capital, imo.