Customizing tab stops

[kj]

In a Fundamental-mode buffer, inserting a tab causes the cursor to
jump to the next tab stop.  By default these tab stops are at
positions 8, 16, 24, etc.  I would like to customize these spacings
for a particular buffer.

I thought that the variable tab-stop-list would do the trick.  So
I made it local to the buffer, and used the command edit-tab-stops
to edit its value.  Originally its value was the default

(8 16 24 32 40 48 56 64 72 80 88 96 104 112 120)

and I changed it to

(16 27 58 68)

...but the display of the buffer was not affected; i.e. the
tab-separated fields in the buffer remained at the default tab
stops.

I realize that the customized local value of tab-stop-list does
affect the behavior of the tab-to-tab-stop command in this buffer,
but this is not what I'm interested in.  I want to affect how Emacs
*displays* the text that follows a tab.

Is there a way to customize such display? 

TIA!

Kynn
-- 
NOTE: In my address everything before the first period is backwards;
and the last period, and everything after it, should be discarded.