I think lumber and plywood is a good way to go for something like this.
If it were me I'd probably build a shallow pan the size of the footprint of the cage and maybe 1 to 2 feet deep depending on what you plan to use as substrate.
Then I would build three walls that could be bolted onto the pan and together. If you only skin the interior walls with plywood and leave the framing open on the outside it will be easy to access these bolts.
Then a door of some sort.
Another thought is to track down pictures of the monitor cage that Junglehabitats built from poplar and glass panels. Basically he built six panels and held the entire thing together with Kreg pocket screws. Each panel was glued and screwed together, but when they were screwed to each other there was no glue used.
Very attractive cage and now that I've experimented with pocket screws I imagine it was pretty strong.
You should email him and see if he'll post here.
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Currently keeping a small collection of various Gonyosoma. Both G. janseni and G. oxycephala.