The problems I had, was that I didn't want to bend the slide by prying from the inside and the screwdriver sliding off the peak of the tab. The thing that worked for me was to use a drift punch.
This one worked out great, I think it was roughly 9/32". The feeler gauge idea was good too, but I'm not sure where mine is and it is not anywhere near as long as the example posted.
Now, the reason I wanted to remove the drawers was because I wanted to see what the inside looked like. I removed 2 and this is what I saw.
There is a secondary wall inside that the slides are attached to.
I had hoped to add a handle to the side and wanted to use a piece of sheet steel as a backer to spread the load across the side.
But, with the added wall on the inside and where the top of the handle was going to line up for a centered handle, around the base of the top floor. I decided against the handle.
My alternative, I have two of these boxes that I bought individually when I started collecting tools.
Living in an apartment, and getting the second box, where to store them became an issue. So, one day at work I was rummaging around the workshop when I came across a piece of cut plywood. I found a couple of cut 2x4's and made this.
The other box is unavailable at the moment, but it works with any tool box combo, like this.
So, I guess, I will fall back onto a secondary plan and install the handle on this box.
I want to make it easier to carry when loaded with tools, also less stress on the rivets in the top handle. And, when carried in the back of my Jeep, it will be easier to grab the side handle and drag the box to the tailgate from outside the vehicle.
I've also been drooling over these three boxes, and this is just way cheaper.
https://boxousa.com/collections/hand-carry-boxes/products/copy-of-3-drawer-hand-carry-tool-box-white-body-with-gray-drawers-black-drawer-trim
https://shop.snapon.com/product/Metal-Boxes/Metal-Box/KRA21G
https://shop.snapon.com/product/Metal-Boxes/Small-Metal-Box/KRA25D
Thanks for all the replies and ideas.