Is it possible to add more plywood of the same thickness to extend the available surface?

You can generally put two "2-wire" cables in a single typical metallic NM connector.
Perhaps you can double up on a few in the top?

I can add plywood, though I was hoping not too since I've already returned the hammer drill I borrowed for use elsewhere in this basement remodel. I can probably manage using a regular drill for just a few tapcons.

I've seen that conduit is required in unfinished basement areas with outlets. Is conduit required by code when running cables down to the sides of a panel?

Stapling or otherwise fastening the NM directly to the surface of the masonry wall would be frowned upon by most inspectors, although I have not found a specific mention of this in the code. The conduit offers some protection and is a convenient way that is about as attractive as any low cost method available. Conduit would certainly be permissible for the cables to your panel. If conduit is used, a bushing must be installed at the other end of the conduit to protect the cable from the edges of the conduit. On the surface of plywood surrounding the panel has been accepted by every inspector I have encountered.

Thank you so much. I will add plywood and secure the cables directly to it.

I've looked in electrical how-to books, even tried to interpret the 2005 NEC, but couldn't resolve this issue. Ulimately the inspector will decide, but at least I will not do something unheard of.

I'm really glad to have found this forum.

As a longtime DIY, one of the shortcuts I've found for determining what's allowed by code - and getting good ideas - is to check out friends' recently built houses. That's where I first saw the use of conduit stubs for bringing several runs of NM into panels, for example. I'd never heard of it until then.

Careful though - once in a while you'll find some violations in new construction.