I'm talking to a Liberal: someone who doesn't actively seek to dismantle capitalism as a system of ownership, production, and the hierarchies within it

This is where you would be incorrect. I very much follow John Stuart Mill (noted Liberal) and others on this question, which I can probably best summarise as: why would you want to liberate yourself, only to subjugate yourself to a capitalist boss at work?

No, I very much favour a transition toward cooperative models of business ownership and ultimately, something resembling market socialism.

I lump all Liberals together and dismiss them out of hand because they're all equally useless.

Which I think is unfortunate, as it ignores the work of many great Liberals.

But the real question that rests at the core of those two issues is whether or not you are trying to obliterate capitalism as a system of private property, hierarchy, imperialism, and rent-seeking, because markets and cooperatives are no means anathema to that goal, but if you're pursuing those projects outside the specific backdrop of ending capitalism then yes, you're still a Liberal.

First and foremost, I am very much a Liberal and at no point have I nor do I deny that. My view is a market oriented socialism is a natural bedfellow of liberalism in the liberation of the individual. I am, as many/most Liberals are, sceptical of an overly powerful state and believe that power should be distributed as widely as possible, within the hands of individuals and communities. Cooperative models of ownership, broadly conceived, fits within that socio-political goal quite nicely.