Gall Force: Eternal Story (aka first movie)
The others suck but the first movie is great. In fact it's still one of my all time favorites.
El Hazard
Again a show where the first OVA is good the followups not so much. Though based on some of the animes you like there is a chance that you are one of the few who would like the TV series.
Also El Hazard is unique in that there is a good dub for it.
Magical Knight Rayheart
I can only recommend the first season again, but that's because I haven't seen the second season yet.
I second some of the recommendations made by others (Nanoha, Scryed, FMP, etc)
If you have seen a lot of the old anime you will like Project A-ko.
Based on your top 20 I'm hesitant to recommend Record of Lodoss war but you might like it.
Something that I doubt you will like based on your list but throwing it out there for other people who look at the recommendations: Gunslinger Girl. It's extremely depressive, yet in a weird way also somewhat upbeat (which serves mainly to make it more depressive).
There are some other I want to recommend but I can't remember them of the top of my head.
E: "Did they... did they just endorse the combination of the JSDF and US Army by showing them as two lesbian lolicons moving in together and holding hands and talking about how 'intimate' they were?"
B: "Have you forgotten so soon? They're phasing out Don't Ask, Don't Tell."
The others suck but the first movie is great. In fact it's still one of my all time favorites.
El Hazard
Again a show where the first OVA is good the followups not so much. Though based on some of the animes you like there is a chance that you are one of the few who would like the TV series.
Also El Hazard is unique in that there is a good dub for it.
Magical Knight Rayheart
I can only recommend the first season again, but that's because I haven't seen the second season yet.
I second some of the recommendations made by others (Nanoha, Scryed, FMP, etc)
If you have seen a lot of the old anime you will like Project A-ko.
Based on your top 20 I'm hesitant to recommend Record of Lodoss war but you might like it.
Something that I doubt you will like based on your list but throwing it out there for other people who look at the recommendations: Gunslinger Girl. It's extremely depressive, yet in a weird way also somewhat upbeat (which serves mainly to make it more depressive).
There are some other I want to recommend but I can't remember them of the top of my head.
E: "Did they... did they just endorse the combination of the JSDF and US Army by showing them as two lesbian lolicons moving in together and holding hands and talking about how 'intimate' they were?"
B: "Have you forgotten so soon? They're phasing out Don't Ask, Don't Tell."