Upload & Sell: Off
I agree with manual flash, but another way to do it is to get one of the brighter, more specular pieces and push the exposure higher (to the right on the histogram) until you see clipping. The clipping may or may not matter to you for the really specular highlights, but assuming it did, use that exposure for all the pieces. One fine point to this is you can actually go up a 1/3 or 1/2 stop above the point where there is no blinking light on the LCD (the clipping signal) because the LCD is 8 bit, whereas many (most) professional level cameras are a higher bit depth .. 12bit, 14bit, which means more highlight data is preserved in the file than what you see on the LCD. So even with the very initial signal for clipping, you can leave the exposure there (test it out by viewing it in Photoshop or Lightroom if it makes you nervous). And then I'd leave the setup the same for all the products, as long as they fit the setup, so as to keep the background even from shot to shot (without having to do much in post). If you have a 300lb piece that doesn't fit, then you need to adapt of course.
The above will work, will preserve you highlights, and will max out the data in your files. I would think it'd be the way to go with speedlights, being fast, easy, and relatively fool proof.
Having done the above, with your highlights preserved, in Lightroom I think I'd up the "highlights" significantly, while pulling back the "whites", such that the background becomes more white while at the same time preserving the highlights. Basically pull up the highlight slider (or use curves) until the background is as white as you'd like, and then pull back the "white" slider until the clipping signal goes away (I use the right triangle in the histogram as the signal). Same could be done in Photoshop, but the easy part of Lightroom is that you could quite easily apply this to all the shots at once with a sync, just as you would white balance, etc. I haven't done what you're doing with 10K parts, but I suspect it'd be pretty easy (10K of anything notwithstanding), not involving much post work.
I'd be better in RAW, but here's a manipulation of the above photo with highlights pushed up 100% and the white slider pulled back 43% (second photo):
I think the whiter background looks less muddy than the grayish original one. To me it looks more professional. It'd be hard to accomplish this simply with lighting. I think you need some post processing, as it allows you to compress the data on the right without blowing the highlights.
With studio strobes, I'd use a flash meter for an incident light reading, as it would be fairly easy to do.