First of all I'm not really convinced by the premise of the question, in the sense that looking for a "perfect" encapsulation of a political idea in the past is something that is almost bound to fail, because the status quo of any political system is always sort of an amalgamation of lots of political ideas and practices.
Which either means people describe something through rose colored glasses (conservatism, reactionism,...) though with a questionable relation to reality or that it is something very shallow or meta which leaves a lot of leeway for possible implementations. Either way an historic example is almost bound to fail with regards to exmplifying a political philosophy.
The other problem is that from what I get from the Wikipedia article, "liberal conservatism" doesn't even sound like a coherent political idea to begin with.
Both liberalism and conservatism are ideologies, they have a sort of "Weltanschauung" (world view), that is a bigger picture of what human nature is, how the world is and in consequence how it should be. While "liberal conservatism" seems to lack that at least from what I can see.
That is in a conservative mindset there is a focus on order, on hierarchy, inequality as the natural stratification of society. Of humans as imperfect an in need of a strong hand to guide them. Often times with a corporal structure (corpus = body) so one unit with a head, extremities, a core etc. in order to justify and explain the hierarchy.
While in liberalism every individual is their own body and essentially equal in value, rights and freedom to every other human being. So the whole hierarchy is unjustifiable and instead the push is towards self-actualization and liberation on the one hand while coping on the other hand with the question how to do that without becoming an overlord to other people who would then justifiably try to liberate themselves from you.
Which in turn gives rise to ideas like, democracy, pluralism, republics, social contracts, etc.
However there is a "minor" problem with "liberalism" and that is that in it's full fledged enlightenment utopia, it could look like some version of communism or anarchism (ideals not practical applications), where there are no institutionalized powers, all power rests within the individuals who form mutual collectives (social contracts) and decide (direct) democratically and without suppressing the pluralistic ideals of it's members how they want to progress.
While in it's practical application it far more often than not resembled more of the old regimes that it succeeded. So much so that you can ask the question what "liberalism" even means, does it refer to the enlightenment ideals of liberty and equality or does it refer to the practical political advancement made under the banner of that ideology.
Did "classical liberals" just fail when they weren't able to outlaw slavery, colonialism, racism, when they didn't manage to erect direct democracy and didn't even provide universal suffrage, when they crushed a hierarchy with the flimsy justification of the church and erected another one with the equally flimsy justification of "meritocracy"? Did they simply not foresee that privileges and property would be the new hierarchy and that free markets of unequal players would perpetuate and increase inequality crushing equality and thus freedom for the vast majority of people... again. Which is entirely possible, I mean these things were kinda new and had never been tested so they could have in good faith failed at their objective, no shame in that.
Or were they working as intended? Was it never the great liberation of the individual, but always planned to be just another coup d'état of a privileged upper class that wanted more rights for themselves, but never actually attempted to have them be universal. Was it less of an intellectual and social revolution and more of a shift in terms of what constitutes the power in society and who wields it, in that case a shift from hereditary aristocracy of the large scale agrarians towards the industrial capitalists.
Because if it were the former than "liberal conservatism" makes no sense. The two are fundamentally opposed in their Weltanschauung and pretty incompatible. While if it were the latter then this would pretty much just be conservatism in a new technological era with a new narrative, but with essentially the same features as before. It would still hail an inequality as a natural order, it's just that the ordering parameter has changed. Previously land ownership, now money.
So "liberal conservative" sounds more like regular conservatism in a setup where liberals won. So a version of the the "Mom, can I have X. We have X at home" meme. Like the classical liberal guys wanted a free market, because not being your own boss and working the fields all day just for your land lord to come by and steal a part of your stuff for himself kinda sucked. So obviously that means that you want a system like industrial capitalism where, the vast majority of people are employed (not their own boss) and work all day to produce stuff just for your boss to come by and steal part of your stuff for himself... wait a second... Technically it's even worse because previously you build the stuff and then a particular part of it was stolen, so people could resort to hiding or whatnot, but now your boss gets the whole thing and then decides how much they would like to give you (potentially hiding a lot for themselves).
And before someone thinks that "Yeah, taxation is theft!". The subtle difference is that taxes aren't an obligation free benefit for your overlord, but that at least technically in a democracy it's a way for citizens to pool money to collective tackle bigger expenses. So you can technically participate in both the debate on how much should be spend on that and where it goes to.
So in other words liberal conservatism is just regular conservatism which cherry picked the liberal portfolio of ideas to accomplish what conservatism was before without that nasty label that became very unpopular during the enlightenment.
Or maybe they actually believe that after 1000sands of failed attempts, this time a free market will accomplish trickle down economics? (fingers crossed)
Maybe they actually had higher aspirations but were reality crushed their dreams and they felt forced by circumstances to do the same or similar things as the rulers before them? Lots of political system cite that anecdote.
Either way in neither of these cases would any existing system be a perfect encapsulation of their ideology and in most of them there wouldn't even be an ideology to begin with, but people are just trying to manage crises. So their ideal solution to unideal circumstances thus not really an ideal system.