Who would have thought to find a Intersil IC in there?
They were the guys who originally brought out the ICL7106/7107 3,5 digit DVM IC's that used to be used in nearly every cheap meter and still are often used in panel meters.
This is obviously a custom numbered IC for Fluke, but could it be.... ?
I did a quick google and came up with this:
Andrew July 4th, 2009 at 02:28
Fluke is not new to off-the-shelf parts and using refence desigsn.
Models from the stone age, like the Fluke 8020, 8022A, 8024 have a main IC called 429100. That one happened to have the same pin configuration as the Intersil ICL7106. The circuits of the meters are very much Intersil reference designs. And not surprising, the 429100 is supplied by Intersil. Guess what IC it really is, just with a magic Fluke custom number …
And guess where I found it? Right here
http://www.eevblog.com/2009/06/29/eevblog-15-part-2-of-2-fluke-189-289-multimeter-review/ 
If he is right, I don't feel bad about the fact that I'm currently building a special panel meter with 4x 7107's instead of the more modern approach of using some micro

.
If it is a 7106 it should be possible to replace it with the 7107, wich drives a LED display.
But it is not a drop-in replacement, you will need to check supply voltage, you will need a +/-5V supply for the 7107. Those IC's prefer their inputs floating with respect to the supply, that can be a bit of a headache.
You would probably have to make your own small board and put the 7107 and some othe stuff on it. But it sounds feasible and quite fun.