A puzzle I made!

[SevenSpirits]

This past weekend was Microsoft Puzzle Hunt 17. I and three friends contributed a module, including two puzzles by me. Here is one of them.

https://www.dropbox.com/s/sr463rco5at7h9...1.PDF?dl=0

[SevenSpirits]

Clarifications:

Q: What's the context?
A: The puzzlehunt was themed as a music festival. Each module of 5-12 puzzles was themed as a musical group - we chose Queen. Each puzzle in our module is named after a song by Queen. All this is why, for example, our puzzle says "Queen" on it; it's not important for solving the puzzle.

Q: What are the "answer check" lines?

They are enumerations of the answers to the clues; e.g. (7 3) means one of the above answers is a seven-letter word followed by a 3-letter word.

The enumerations in each section are in alphabetical order for your convenience.

The answer check lines are strictly unnecessary to solve the puzzle, but they sure do help you confirm your answers to the clues.

Hints:

Q: What do I do at the start? Help, I've stared at it too long and can't figure out anything! Just give me one example.
Solution for the bottom clue:

LIVE LONG AND PROSPECT

Q: I solved all or almost all the clues but I'm totally stuck on what to do with them. Give me a hint?
Hint 1:

Notice anything interesting about the single letters you replaced? (See hint 2 if you're stuck.) How about the pairs you are subbing in? For the latter, living in the US may help. (See hint 3 if you're stuck.)

Hint 2:

There are only six different ones. Can you get an ordering from them?

Hint 3:

They are all US state abbreviations.

Hint 4:

You'll need to draw the 6 "race courses" on a map.

[Ichabod]

Thanks, Seven.

I'm trying my best to solve it, but I'm pretty lost right now. I'll try for at least some more days before using the hints, since I have some pride that I'm clinging to.

[novice]

Nice puzzle! I think I'm on to something:

Start:

Templar tantrum - E + LA
Neigh of relief - S + NE
The Art of Wail - R + IL
Sails serif - N + IL
Painter is coming - W + PA
Cannery in a coal mine - A + NE
A / N / S / W / E / R

States, sorted by ANSWER:
A NE Nevada
N IL Illinois
S NE Nevada
W PA Pennsylvania
E LA Louisiana
R IL Illinois

2:

Swiss chemise - E + MI
Cactus Belli - S + CT
Dialing Philosophers Problem - N + AL
J. K. Scowling - R + SC
Planet of the wipes - A + WI
Prince of Scales - W + SC
S / N / R / A / W / E

States, sorted by ANSWER:
A WI Wisconsin
N AL Alabama
S CT Connecticut
W SC South Carolina
E MI Michigan
R SC South Carolina

3:

The fiscal countdown - N + SC
Schindler's Limit - S + MI
...A something drum for holding a cold treat (3 5 5)
Rings to riches - A + IN
Jack the flipper - R + FL
. / R / A / S / N

States, sorted by ANSWER:
A IN Indiana
N SC South Carolina
S MI Michigan
W/E
R FL Florida

4:

Morale code? - S + AL
Mice in the hole - A + MI
Gaussian roulette - R + GA
The Vampire Strikes Back - E + VA
Tragedy of the commodes - N + DE
R / A / S / E / N

States, sorted by ANSWER:
A MI Michigan
N DE Delaware
S AL Alabama
E VA Virginia
R GA Georgia

5:

solder eclipse - A + DE
Live long and prospect - R + CT
R / A

States, sorted by ANSWER:
A DE Delaware
R CT Connecticut

Observations:

All the inserted letters are US states.
I'm guessing we connect them on a map to draw letters that spell out the final answer.
Also, all the removed letters appear to be in the set A / N / S / W / E / R