I am using TASM I think... or possibly SPASM.   The problem I am encountering is that the .org statement physically moves the code to that region instead of telling the compiler to reference all future labels from that origin.  Like for instance, if I do:

.org $0000
.dw  $F00D
.org $0000
.dw  $CAFE
The the first bytes of the executable will be $CAFE, but $F00D will be ignored.  Likewise, if I do:

.org $0000
.dw  $F00D
.org $9002
.dw  $CAFE
The first bytes will be $F00D, followed by $9000 zeros, and then $CAFE

What I would expect is that both should output just $F00D and then $CAFE as the origin should only tell the assembler what to do with labels and not to actually affect the compiled code.  Is there some other assembly directive or macro that behaves just like .org but doesn't physically move the code around?  I tried searching but I couldn't find one.

TASM supports nothing of the sort to my knowledge. To do relocation, you have to do something like this:
destination .equ $9001
.org $0000
.dw $CODE
;relocation
relocate .equ $
label:
dec a
jp nz,label+destination-relocate
In short, you need to define a couple equates and use +destination-relocate with any non-relative address (anything that's not jr or djnz)

Ok, I'm trying out SPASM, but every time I try to compile, the entire "ti83plus.inc" file is highlighted in red but with no error message and the code and data sizes say 0.  What do I need to do to make my TASM z80 file SPASM compatible?

do you have .nolist #include ..... .list ?

Have you ever used Wabbitcode? It's and IDE for ASM. It's still Alpha version, but it works. http://wabbit.codeplex.com/releases/view/45275
Use Ctrl+B to compile.

Hmm... I still have a strange problem.  The .db and .dw directives don't seem to be working.  It compiles with no errors, but I go to open the .lst file and even though the program counter is advancing correctly for the data, nothing is being outputted to the binary.  Here is an example:

   93 00:000A -  -  -  - 
   94 00:000A -  -  -  -
   95 00:000A -  -  -  -  .dw $6DBB
   96 00:000C -  -  -  - 
   97 00:000C -  -  -  -
   98 00:000C F3 -  -  -  di
   99 00:000D -  -  -  - 
  100 00:000D -  -  -  -  Loop:
  101 00:000D 3E -  -  -      ld a,1
  102 00:000F D3 -  -  -      out ($20),a
  103 00:0011 FD 21 -  -      ld iy,plotsScreen+384
  104 00:0015 21 -  -  -      ld hl,Length

The data directives aren't being added to the binary like the instructions are, I even checked the binary to make sure it wasn't just an output error with the list file, but they're not there either.