I'm afraid I won't be of any real use since I've never seen a drama from the 90s before but I have a couple from the early 00s that I'd recommend..
Since they're quite well known, I'm not sure if you know them already (your completed list is a bit empty :P), hope it helps anyway!
Kimi wa Petto (2003) strong & sucessful woman adopts young guy as her dog
Anego (2005) office romance between older lady & younger guy (Shinohara Ryoko is amazing in this, I love her)
Sore wa, Totsuzen, Arashi no you ni.. (2004) again older lady & younger guy romance (it seems like I was into these stories back then or it was just a hype lol)
Nobuta Wo Produce (2005) girl that is bullyed in class is given a make-over by most popular guy in the school and his weirdo friend (there is some romance if i remember well..?, but it's mostly friendship - it's hilarious though :P)
1 Litre of Tears (2005) tear jerking drama about a girl with an incurable disease
good luck with your search!