As you're suspecting, the components will actually create quite a bit of heat - my PS3 is like a furnace!
I think that you have the equipment on the right shelves - amps on top, then sources, then the surge protector on the bottom.
One of the challenges you have with the solid shelves is getting airflow/circulation - you have to be able to get air in, over each piece of equipment, and then out. One solution would be to drill a series of decent-sized holes in each shelf to allow bottom-to-top flow of air or you could keep the shelves intact and do a left-to-right flow.
You'll have to use a fan (or fans) to move the air - passive convection won't be sufficient (especially when you shut the doors!). You said there is a sub-floor under the unit - and under this is the basement? If so, that's great - you'll have an almost unlimited source of cool air; it also gives you you opportunity to mount the fans outside of the cabinet, making them inaudible.
I can't see exactly from the photographs, but it looks like you may have space in the very top of the enclosure to build a "false ceiling" - kind of a plenum chamber - that you could then vent back down to the basement if you went the "bottom-to-top" venting route.
I don't know how much detail you want to get into, but here's a great document from Middle Atlantic (the "rack people") that does a really good job of discussing some of the fundamentals of what you're trying to do:
Not sure if any of these ramblings help, but at least it's a start!