As you pointed out at the beginning of your post, the view of politics you have presented is a reductionist one. Unfortunately, this makes your question difficult to answer for a lot of people, as "political compass position" does not describe their political views very well. I suspect that we have many members who fit this description.
I think economic matters come down to ideology that can't really be proven one way or the other.
There has been a concerted effort to convince people of this, and I feel that it's really unfortunate. So many things in our lives are implicitly economic, and most economy has underlying politics. Mainstream (neoclassical) economics, of course, is unlikely to tell you much about what's going on. It has been repeatedly pointed out that much of neoclassical economics does not uphold standards expected of scientific research. Since the fiscally liberal / fiscally conservative dichotomy lives in this world, it is unsurprising that it comes off as a bunch of thoroughly baseless ideological proofs. This, however, does not mean that nobody is studying economy, or that any attempt to analyse trade and production is pure ideology.
There is, I guess, also the hidden assumption in your model that economy is not social. And that a particular kind of change is progress & is good. If progress is merely positive social change, I don't think that any group would consider themselves "conservative". I can only really say that I don't agree with most (any?) of the ideas I've heard put forward under the banner of "conservatism", and I find many aspects of liberalism distasteful too.
I am not really an expert on political ideological groupings, though. I am much more interested in the details than the Who To Vote For and the Who Knows Who of electoral politics. And my details have a lot of "I don't know yet"s in them. Perhaps someone more capable of conviction can answer on more concrete terms.