The color balance can be converted from very red to more neutral with the eye dropper tool in the basic panel. In the example, you could click the eyedropper on the man's white shirt. Other photos might not have a part of the photo that was originally white or neutral grey, so clicking somewhere with the eyedropper won't work, and then you'd have to play with the temperature and tint sliders until you get something you like.
As explained at that link you gave, the cyan dye has mostly disappeared and so information from the cyan channel is probably gone forever, and I doubt you'll be able to return the photos to natural looking colors without a huge amount of work, if then.
My gut feel is that Photoshop would be a better tool for this task if you intend to do a lot of work on each photo — Photoshop has a lot more tools that might help. If you're planning on just spending a minute or two on each slide, then Lightroom will probably do some good things.
I have been focussing on WB and then setting whites & blacks for optimum .........sometimes adjustment in HSL will work ... but not often.
I no longer have PS (last had a copy when it was PS 5) ... LR does what I need for all my own pictures, and can't justify immense cost of PS (unfortunatly)
Is the slide that red? I use a Canon scanner and I use the same scanning software you are using. I have set default settings for my scanner that it seem to work fairly well. I also scan as TIF images. When they are imported into Lightroom I have chosen to have sharpening and radius pushed all the way to the right, and I automatically move the clarity to +20. I have VueScan set to default settings as far as color is concerned. I find that quite often I will choose the Auto setting in the basic panel. Anyway, those settings work fairly well for me.
I am not the thread own, but I also want to answer.
For slides I use my DSLR and a macro lens together with projector. This works great and gives me the highest resolution.
For paper prints I use a scanner and try to ajust as much as possible in the scan software without loosing information.
I have often wondered about doing that. But I don't have a projector anymore. I suspect I would probably get sharper images if I could do that. I can get plenty of resolution, that's not the problem.
I find that with people in picture pushing clarity gives poor results on faces
Interesting your comments on sharpening .... I'll give it a try