Your results seems fine, haswell quads run extremely hot, specially 4770/4771/4770K that have enable hyperthreading, mine can reach close to 80C with a big cooler like the HR22, so your results seem well in line with a smaller case with limited cooling.
Should I try reseating the heatsink? I fiddled around with it a lot trying to figure out which orientation so maybe it isn't making a good thermal bond as I applied the heatsink to the CPU several times without reapplying thermal paste. Should I pull it off and reapply the thermal paste?
You should always reapply thermal paste when when you uninstal/reinstall the heatsink, paste will spread and when you re place it air bubbles might interfere, the contact might not be as good, themal paste like Artic MX-4 its very cheap and you can do a lot of installations with a single tube.
One thing to consider is deliding the chip, some people have gotten more than 15C drop outs from redoing the paste inside, this would void your warranty and there is a chance you will damage the chip, only you can decide if its worth the risk or not.
Alpine 7GT 90x86x66 (rated at 70W but can be oriented either way)
Big Shiruken 125x135x58 (probably too big unless the RAM clearance of 33mm is enough which is doubtful)
Shuriken Rev B 105x116x64
Noctua NH-L12 128x125x66
Zalman CNPS2X 84x84x27
Out of your list, the best is the Noctua NH-L12 but since you mention you cant use it with the top fan, it will get diminished a lot, so i wouldn't consider it unless you find a way to use the top fan.
While im not a big fan of TomsHardware reviews, they did recently a review of a lot of low profile cooler, and has some that you are considering, might be worth a look, Eight Low-Profile CPU Coolers For Your Compact PC, Reviewed
, in it the NH-L12 seems like the best but again since you cant use it due to height restriction on the top fan, i would probably check out the ZALMAN CNPS8900 Quiet
has a height of 60mm, and its cheap. That said i dont think you will get much better temps just with the cooler, its more the chip that run hot and needs bigger heatsink and more airflow.
You should get lower temps on a slightly bigger case like LIAN-LI PC-Q11] and fit a tower cooler like Scythe Mugen 4
, this will make fitting a standard PSU impossible, but a picoPSU should do the trick like PicoPSU 160XT
, lian li even sells covers for the back PSU section like Lian Li Vented Power Supply Bracket Cover - Silver
, or you can make one with plastic/metal plate.