Based on a game by Alice Soft.

As an old anime fan I’ve become very picky in what I watch and have tried most mainstream titles. Can anybody recommend me a lesser known anime that has a contained story with an ending that doesn’t rely on typical anime tropes to be entertaining?

Just afew for now but I found quite a few.
Try NOIT which relies on a very unusual plot and storyline but it is quite bloody and violent.
Texhnolyze is very similar to the Phantasm horror films which were rated R.
JinRih:The Wolf Brigade relies on a retelling of the original Grimm Bros Red Riding Hood.
Not the sweet Wolf as Granny and Woodsman bit but the original tale not very well known.
Monster is a serial killer tale and also relies a bit on this same Red Riding Hood tale.
Trinity Blood and Blood Plus are based on vampire-like creatures.
If you like police shows and don’t mind a short 3 epper series Gunsmith Cats is great.
You can’t go amiss w/ Cowboy Bebop and Outlaw Star.
Set in the same era of the future, both involve space travel and feature unusual characters and great voice work.
If you like cops, Interpol, space travel and comedy and don’t mind violence and a few cuss words tossed into the mix, Dirty Pair, DP Flash and Crusher Joe are your tix to fun and games.
These 3 anime series, films and OVAs turned me onto anime when I was approaching 40 in 1985.
They led me to a love of all things Japanese, my own fanfictions I write and post and aa love of anime as well.
Rhe Naruto tales, Trigun (Old wid Western anime on another world) and OnuYasha for a period piece w/ lots of time travel and fun and comedy as well as a heart-touching plot(s).
round out my recommended list but there are many more such as Strait Jacket which is quite psychological and similar to Hitchcok’s old horror films.
These should get you started, my friend.