> Multiple access points to flood an area.

Better describe "the area".

> I suspect the problem is interference from numerous other wireless devices
> in the area.

Possibly. But without describing where you're trying to do this it's
impossible to say. If you have any control over the other devices it might
be possible to reduce the amount of interference. But if they're not yours
and you can't contact who's running them then it may not be possible to do
what you're after. Rather it might be possible, but perhaps only with more
access points, each running at a lower power.

Likewise if the interferring systems don't need to be covering such a wide
area it may be advantageous for THEM to reduce their own radio power levels.

> A possible solution would be to position two separate wireless routers
> (access points) toward the edges of the area with each wireless router
> (access points) hardwire linked to the modem via (possibly an Ethernet
> switch and) CAT5 cable.

Without better info it's impossible to say if that's right or not. But yes,
in general, you put an access point where you want coverage and run wire
back to the switch.

> My current wireless router / access point of choice is the D-Link DI-524.
> It has been chosen because the native IP range 192.168.0.X of the D-Link
> does not overlap the 192.168.1.X IP address range of the router built into
> the 2WIRE2701 modem (wireless option disabled)

All devices of this sort have configurable options for their IP address
and/or IP range. Chosing one based on that is like chosing a green car
because you think it's faster than a blue one (everyone knows red is faster
anyway. Heh)

> My guess is that I can either: (1) configure each D-Link wireless router
> so they have non-overlapping IP address ranges and feed them in parallel
> from a switch, or (2) disable the DHCP in one of the units, and feed it
> (the second in the chain) from the first unit.

Use one as a router, use the other as an access point. They can be on the
same subnet, just make one of the run DHCP and disable it on the other.
DHCP requests will be passed through one to the other via the wired ethernet
connection. An access point is basically 'dumb' in that all it does is pass
traffic from the wired network to/from the wireless clients connecting to
it.