What I have found is that you'll need to write macros for each form field:
I did a different work-around for my own form. I set it up so that the field I wanted to tab to was below the current, highlighed field. If you use a table, it'll work.
I created a three-cell table and divided my information accordingly across them. If you create more than one row, tabbing will go across--and you'll even land on cells where you can't make any entries or changes--so make sure you have a one-row table with columns across.
In each cell, I used a carriage return to add more information/fields. You can use CTRL+Tab to tab within the cell while you're creating your form for a nice, formatted look.
I used the LEGACY text form field, not the updated Word 2007 one (on the Developer tab in the Controls box, you'll see an icon of a file folder with a couple of tools criss-crossed in front of it).
Once you protect the form, you should be all set. I imagine you could play around with rows and columns if you need to tab across the form before tabbing down, but you would probably be limited in your options.