lightroom - Why can't I get a pure white background, even using multiple light sources?

Edit: THIS IS NOT a duplicate of Why can't I get a decent white background with product photography?. Reading my question and the linked one you will see I HAVE ADDRESSED the issues suggested by the answers of said question, and I'm still not getting satisfactory results. My setup is very different from his (I have four lights and he has only one). My question also talks about RAW not getting blown out whites, the linked question's author makes no reference to RAW.

I've been doing "good enough" white background photography from time to time, for a number of years, using a cardboard box with cutouts, tracing paper, and 3 60W filament lights (yes! and, yes! I burned myself with them too). The results have been more or less acceptable, though they require a little photoshopping afterwards.

Part 1: Gear and Setup

Now I've upgraded my gear a bit. I have 3 YN-560 flashes, a Nikon SB700, an umbrella, and a small DIY softbox. I've also found an interesting piece of plastic to use as a background: it's a diffuser found inside LCD TVs. It's what they use to get a perfectly even backlight for your screen.

I've been trying to get pure white with my new setup but I've had little success. The latest experiment, with the diffuser sheet, was actually worse. The setup I use is:

Plastic diffuser as cyclorama. 1 flash lighting the back, with a black card to prevent spill 2 flashes with umbrella and softbox on each side of the product 1 flash lighting the diffuser sheet from below

The result is this:

Terrible, and not even close to pure white.

A better example is this:

I suppose the problem is the lighting from the underside. In the first photo, light spills from the floor and gives a creepy light. In the second one, the base of the figurine shades it and, and it allows me to better light it from the sides.

The problem is: if I don't light the bottom, I may get a blown white background, but no white "floor". But if I increase the light from the sides, the object starts getting blown out as well.

Part 2: Highlight Warning lies

When I was taking the photos, I managed to get highlight clipping warnings on my background. I thought, great, the figure is fine but the background is blown! Then I went to import the photos into Lightroom. To my surprise none of the photos had highlight clipping. Why does this happen? My guess is the highlight clipping indicated by the camera is based on the embedded preview, and not in RAW data. What I use in Lightroom is RAW, and in raw there is still a little bit of headroom.

I also have a very weird histogram:

This fools lightroom and it doesn't let me use the usual sliders. For example: moving the highlights slider doesn't do much, but the shadows sliders adjusts the brightness of the figurine in the photo (since lightroom considers it to be shadows). Is it possible to edit the photos the traditional way, or does this sort of high-key photography always fool Lightroom? ...or does Lightroom think I don't want clipping on my images and it's doing something weird on import?