By the strict definition of "sentimental", this is a list I felt regards towards.
Romance driven
-Ai Yori Aioshi (though I am only familiar with the manga)
-Baka to Test no Shoukanjuu ni! (wasn't in your "completed" list, cristmas special and ova as well)
-Code-E
-D.N. Angel
-Da Capo (I stopped following with the original)
-Dual Parallel! Trouble Adventures (and "Special"/ova)
-Elemental Gelade
-Futakoi Alternative (didn't like the original much)
-Futari Ecchi (only familiar with the manga)
-Golden Time (the first half...)
-Gosick
-Honey and Clover (season 2 and such)
-Hanasakeru Seishounen
-Howl no Ugoku Shiro (Howl's moving Castle)
-Iketeru Futari (Only familiar with the manga)
-Kanokon (I prefer the manga but meh)
-Kareshi Kanojo no Jijou
-Karin
-Koi to Senkyo to Chocolate (may be the opening song in this case, love the
Opening song)
-Love Hina (Loved the manga, hated the anime)
-
Tragedy driven
-Air (by Clannad creators)
-Cossette no Shouzou
-ef: A Tale of Melodies (only watched first season, haven't tried the rest)
-Fruits Baskets (hard to decide if this pile or romance...)
-Full Moon wo Sagashite (only familiar with the manga)
-Hoshi no Koi (Voices of a Distant Star, an earlier work of Matoko Shinkai, the one responsible for 5 centimeters per second, this one is still my favorite work of his)
-Iriya no Sora, UFO no Natsu (there was something about this series I didn't like, I can't remember though, quite similar to Elfen Lied, so I put it in here thinking you may enjoy it)
-Kanozuki no Miko (everything else the creator did after this was simply shocking, disappointing and depressing for me, but I loved this)
-Kanon (original and/or remake, by Clannad creators)
-Kimi ga Nozomu Eien
-Kono Minikuku mo Utsukushii Sekai (This Ugly Yet Beautiful World, I need to re-watch this myself, but along the lines of Elfen Lied if I remember correctly)
-Kumo no Mukou Yakusoku no Basho (The place promised in our earlier days, another work of Matoko Shinkai)
-Loveless (Yaoi)
-
Action driven
-Blue Gender
-Blue Submarine No.9
-Card Captor Sakura
-Chrono Crusade
-Escaflowne (the movie)
-Kara no Kyokai
-Kaze no Stigma
-Kurozuka (Had a hard time with this section and tragedy, only familiar with the manga)
-
Slice-of-Life driven
-Chocotto Sisters (familiar only with manga though)
-Kamisama Kazoku
-
related to your list
-Kujibiki Unbalance (an adaption and a spinoff from Genshiken, didn't appeal to me though)
-
This is out of series I've seen to (or at least near up to) completion, and from them, the ones I felt legitimate "sentimentality" for. So with the already existing possibility of my taste being different from yours, my taste may differ from itself, seeing as this accounts for my many years of watching anime, my standards may show in the quality of the shows I've listed. I have grown quite high standards in recent years, but I have attempted to take into account myself a few years back to remove too much bias and pretentiousness from my recommendation.
Side note: This is checked against your completed list, so forgive me if I miss it in your watching/planning too.
Side note again: This list is constructed from series with the "romance" tag attached, I figured the general list would be too long for me to cover, (around an 1:20 clocked so far). So any series, that I would have found "sentimental" but are without that tag will not be in the list, unless I explicitly think of it.
Hopefully this helps.
Reason for incompleteness: MAL seemed to have gone down, and I can no longer check the series or your list. I may come back to this, but I am known for never finishing something if I leave it half way done, so apologies if I don't.