Has anyone been able to define well or measure differences between vinyl and digital?

Is there really any proof that remasters have compressed dynamic range (the so called loudness war)? Is it just a mostly baseless term intended to invoke an emotion?

Yes there is. Many Cds have been dynamically compressed since the early 90s. You can find dynamic range numbers for a lot of albums at the Dynamic Range Database:

Album list - Dynamic Range DB (loudness-war.info)

There you can find which versions of a particular album have more or less dynamic range. You can then go to Discogs, an Lp and Cd marketplace, to buy the version you’re looking for:

Discogs - Music Database and Marketplace

Albums are supposed to be listed there by specific reissue so you can find the reissue that is supposed to sound the best or 2nd or 3d best. Check with the seller to make sure his albums are listed under the correct listing before buying. Reputedly better sounding Cds and Lps (e.g.less compressed) sell for more $ and sellers don’t always list their Cds and Lps under the correct listing. Probably just an honest mistake, but I suggest checking before buying anyway.

On a related note the dynamic ranges of Lps and Cds on the DR database cannot be compared directly. It has something to do with the way the site measures DR that makes direct comparison between the formats inaccurate. I’ve read an explanation before, but I can’t remember what it is.

Vinyl sucks.  Measure that

I think it is the physics of analog crosstalk of the cartridge :)

Ps Audio recently posted on this very topic. Perhaps the answers you seek are contained within Paul’s posts. 

"An album with DR 6 doesn't necessarily sound overtly bad. And an album with DR 12 doesn't necessarily sound good (but the DR isn't to be blamed at least). For rock/metal a DR of 8 and above is considered okay. Electronic music can still sound okay with DR 5 because it is less dense."

Ref: https://dr.loudness-war.info/faq

It therefore seems the differences are mainly academic in the same way as ASR tests hardware.

If you don't like listening at 90dB then something with higher compression might even sound better. Indeed the average person seems to listen around 70dB for comfort.