Is there a trick to converting JPG from RGB to CMYK without the lossy re-compression?

Question

So I've got around 750 images in multiple categories and folders. Each image has 6 variants - 16 bit TIFF from over-eager beaver photographer, 16 bit TIFF, extracted backgrounds (done by student workers, who do not use English as we are not in the US), then, standardized 3000x2000 (or other suitable aspect ratio) PNG with corrected edges for web and light print, an 1800x1200 JPG for web and a few smaller PNG standards also for web.
The 16 bit TIFFs with Extracted BG are the root files, and a series of actions builds the PNG's. The standardized PNG's are then pumped through actions and Image Processor to create output files.
So I just discovered that a seemingly random number of these are in CMYK. That hasn't been a problem up until now because our website and our printed materials have no problem with CMYK and RGB files.
But now we are starting to hand out these images to our customers - who are only interested in the 1800x1200 JPG and maybe 900x600 PNG files, which are most easily pulled directly from our website rather than sending them the entire 180gb graphics directory.
And some of them are telling us that the pictures are being rejected. Most notably, Ebay does not allow CMYK files.
So damage control- rebuild our entire library of images from the 16 bit TIFFs
OR
rebuild only a couple of different sizes and upload from there, replacing the pictures on the next major update (over the next year).
I am *NOT* concerned about preserving color since 99% of our products are black and shades of grey, with only a hint of color.
I am concerned about the degradation of changing mode on 60-70% compressed images, then resaving again with the lossy JPG compression.
I'm about to start ripping into things with my actions and replacing around 1500 files online, so I'd like to be sure that I'm doing things in the most sensible way.
If there's a tool that can do this conversion without another pass of compression, that would be ideal.

Answer 1

My understanding of the JPG is only middling. I thought I understood that it uses anchor pixels and either a translation table of some sort or difference mapping, using 8 bits per piece of information.
If that were the case, surely changing the translation from CMYK to RGB would be fairly simple.
In this case, the usage is Ebay and they only accept JPG, PNG (and maybe BMP and GIF, I didn't look that closely), but require RGB. I was actually quite surprised to find that JPG allows CMYK since, as you say, anyone dealing with CMYK is going to be dealing with commercial printing and few people who deal with commercial printing would play around with JPG.
I always stick to TIFF or PSD for workflow, but JPG is popular for a reason - when it comes to web, JPG is the only format that can deliver manageable file sizes with full-screen or "large" images for web. Our top level banner photo is 2590x692 and needs to be under 400kb for sane download speeds. PNG couldn't touch that. Even with the aforementioned 1800x1200, PNG is nearly 2mb, while I can maintain very decent quality with a 500kb file with JPG that works well for 'zoom in' type usage.
So there's no way around JPG. It's just annoying that the first person to touch a random selection of the pics was primarily an Illustrator user and saved *some* of the pics in CMYK mode.
It's like that old story about the farmer who didn't want anyone to steal his watermelons, so he cleverly posted a sign "None of these watermelons are poisoned", only to find a note the next day saying "Now, One of these watermelons is...".
Far more work to fix 'some' of the images compared to just doing it right the first time.
But then again, for workers like that, if you can't trust them with an easy job, you could hardly trust them with more complicated jobs...