Or custom made shoe. Roundover bit in a router. Clear stock. Rip on a table saw to appropriate height.

But don't you have other problems? Like high water jambs & door casings?

I don’t understand why removing the baseboards will tear apart the wall? Aren’t they just finishing nails holding it on there?

your floors look nice, don’t you want the baseboards done right, for a clean look? And, as cilantro mentioned, casings and doors...

This is really easy to fix. Just install nailer strips under the baseboard. That will give you a backer to nail the shoe molding to. If you have a table saw, just buy some wood the same thickness as your baseboard and rip it down.

If you don't have a table saw, buy wood the same thickness and chop saw it down, making sure you have a filler piece at every point where you will nail the shoe in. When you nail your fillers in make sure the nail is long enough to get into the bottom plate.

Thanks all! I‘m going to try the double stick carpet tape @G & S Floor Service as it seems like the path of least resistance and if not the nailer strips @bry911. In response to @ci_lantro and @Mrs. S - I do have high door jambs but I’m willing to live with that (it’s a 100+ yo house, trying to do least invasion possible). Also, the last owner put 64 nails in a single 6’ baseboard so prying it off the wall was hard without making dents in our plaster. Again, thanks everyone!

Or use this. It is 1 3/8” high.

https://www.homedepot.com/p/Alexandria-Moulding-WM946-3-8-in-x-1-3-8-in-Primed-Pine-Finger-Jointed-Stop-Moulding-0W946-93192C/206013363

The double stick carpet tape without the nailer strip is not going to give you enough area for the baseboard to meet up with and stick to the shoe molding. A good bump to the shoe molding is going to dislodge it.

And once you have the nailer strip in place, you may as well actually nail the shoe molding in.

Also, the last owner put 64 nails in a single 6’ baseboard so prying it off the wall was hard without making dents in our plaster.

Oh my. Sounds like someone who just got their first ever nail gun!

A trim puller is on my tool wish list: https://www.homedepot.com/p/Zenith-Trim-Puller-Multi-Tool-for-Baseboard-Molding-Siding-and-Flooring-Removal-Remodeling-ZN700002/206509569