This is not true. Every libertarian think tank that I have ever heard of is favorably represented with in the LP. The LP gets almost all its guidance either directly or indirectly from the many small "l" libertarian (as you call them) organizations and publications. The only small "l" libertarians who reject LP positions ("thought") to any significant degree are extreme anarcho "voluntarists" who reject all group organized activities (including all political parties) on principle as being collectivistic, choosing the Aquarian Conspiracy model of independent action instead. For similar reasons, Randians also significantly reject LP "thought."
The fact that most libertarians reject the LP has nothing to do with LP thought. The rejection of the LP by libertarians at this time is mostly based upon priorities and political strategies. Thus most mainstream libertarians can be found as either Democrats or Republicans.
I think that most small-l libertarian FReepers would disagree. I personally stronly disagree with the LP on borders and foreign policy, and I dislike their neutrality on the abortion issue.