I think many of the HQ board corridors are quite narrow (the squares are 20mm across IIRC), which might be an issue. Also, I reckon you might need more and bigger doors.
However, if you are happy to make you own card stand-up doors, I'd make some bigger ones (maybe double-width) to improve access around the dungeon.
You would need to house-rule certain spells (since the dungeon is assumed to have ceilings!), and which models can fit through which doors. I would also use some crates and barrels mounted on 20x20mm bases to strew around as LOS blockers because I think furniture like tables will make the rooms a bit too cramped otherwise.
If you're willing to do a little extra work though, I think Frostgrave in a dungeon could be quite exciting!
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Failing all that, you could get some nesting cardboard boxes, and spray them grey with a can of primer from Halfords. This provides simple easy-to-store terrain that can easily represent ruins and small buildings in a pinch. You can also cut doors, windows, and ruined holes/corners into them as well (and they will still stack together). The lids can be used as roofs, or placed onto the table for low ruins. Something like
these perhaps? When you're done, they all stack inside each other like Russian dolls.
A grey cloth and a white can of spray paint can make a nice frosty-looking 3'x3' dropcloth for extremely little work.