Do the LDP even have a real platform? Their style of party plain wouldn’t work outside of a dominant party system.
The LDP is basically if the more establishment-y elements of both parties got together and had to sit in one party. Of course you'd have a broadly moderate party with a ton of factional disagreement, which is what the LDP is.
Problem is, America just isn't a place that generally produces dominant-party systems quite as strong as Japan's. America's a land with a very long history of vigorous two-party competition, while Japan, being stability-minded and concerned with continuity, has a stable governing dominant-party that takes the best talent away and keeps in a place a self-perpetuating cycle of power preservation on both national as well as prefectural level.
So if you really want an LDP-style party in America, you need to first think about how it came to be in the first place. It certainly could have come to exist in some alternate scenario, sure, but as they say, the devil is in the details.