I would use the thicker plywood for a cage that size. Maybe even 3/4".
Regarding the dimensions, I think you should consider making the cage a bit deeper front to back and not quite as long. If you shortended it to 6' and increased the depth to 4' you would have the same floor area as what you've mentioned. But there are advantages to the 6x4 footprint.
1) The scrap from the two 6x4 pieces can be used as the sides of the cage.
2) The cage can be turned upright and moved through doorways, etc.
3) Cuts and overall design would be a bit easier to do with 3 full sheets of plywood. If you wanted all of your panels to be cut from single pieces your 7x3x2 would require 4 sheets.
The disadvantages of the 6x4 footprint:
1) Harder to clean a cage with a 4' depth, especially if it's only 2' tall.
2) Viewing is more restricted due to low height and greater depth. Although this may be a benefit from the standpoint of the animal feeling secure.
So I'd say if you already know you have enough room to move a 7x3x2 cage around why not go ahead and make it 8x3x2? Less cutting/waste of material since that's the length it comes in.
And if you have the space it is nice to build them a bit taller. It makes for better viewing, IMO.
Do not use a deck sealer for your monitor cage. They have UV stabilizers and solids that are designed to stay slightly flexible over time. I'm not sure how safe those are.
For a heavy scratching species here are choices in order of cost (cheapest to most expensive) and ease of use (most difficult to least difficult).
The cheap way to go is with fiberglass resin. But that is not easy to work with. I've always regretted it when I used it in order to save money.
West Systems Marine Epoxy sounds like a nice compromise when it comes to cost/ease of use.
Fiberglass Reinforced Panel is probably the most straightforward and the only nusance is the dust created when cutting with a power saw. Heavy duty clippers can be used from what I've heard but I have not tried this.