Good update !

What strikes me as odd is that I thought that valves became tighter with use rather than the opposite.

That being so, I wonder why they were loose?

Anyway, I agree that it sounds like nailing. My 300D sounded more chatter nailing-wise at low RPM and it got better at higher RPM.
Replacing all the injectors resolved it.

maybe you have one or two bad ones?

__________________
1979 300D 220 K miles
1995 C280 109 K miles
1992 Cadillac Eldorado Touring Coupe 57K miles SOLD
********************
1979 240D 140Kmiles (bought for parents) *SOLD.
SAN FRANCISCO/(*San Diego)
1989 300SE 148 K miles *SOLD