Best cartridge for very old worn vinyl

I think you should look at some of the EMT cartridges with spherical styli. They have both stereo and mono models

https://www.emt-tontechnik.ch/cartridges

Do you mean your current cartridge inventory is too costly to use in this instance or they demonstrate an inability to track well? Just to clarify...

Jperry and Chakster have offered diametrically opposing opinions.  From what I have read over years, I think Chakster is more likely to be on the right track.  Those old LPs are most likely to have been worn out with spherical and/or early classic elliptical styli.  So statistically your best bet for getting more music out would be to use a stylus with a different shape that contacts the groove walls differently from a spherical or elliptical. Most modern styli fall into the categories of line contact or microridge, although there are a bewildering number of names for very slightly different shapes, like Shibata. There may be reasons to hunt specifically for one particular shape that would be particularly good at contacting unworn regions of the groove, and perhaps someone else knows.

What they said covers the standard stylus/groove aspect. There’s also the moving mass part, which is why the better high end carts tend to outperform in terms of surface noise. With that in mind I would be giving Peter Ledermann a call at Soundsmith. You can’t be the only one with this problem and he would be the man to make one for you, if he doesn’t already have something perfect just sitting there ready to go.

The London Reference has an extended line contact stylus. I would also talk to London's John Wright to see if he has a stylus he recommends for old worn LP's.