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Dear: This makes it sound like you are near and dear to my heart. I just learned your friggin' name one minute ago so that I can send you this letter.

Sincerely: I really mean "I need something in this space so that you know I'm wrapping up and about to sign my name"

For some reason it bugs me that the standard way to write letters begins and ends this way.

My letters usually start out like this:

To whom it may concern:

Go eff yourself.

Cheers,
TFG

if starting with "Dear Mr. Smith" seems awkward, try starting with

"The Most Righteous Mr. Smith"
OR
"Newly met Mr. Smith, please accept my missive"
OR
"Yea, verily, Mr. Smith, I hail thee in time of need"

instead of "Sincerely, PopeyeCard" try

"Reiterating my joy in awaiting your response,
Popeye Card"

OR

"With kind regards to you, yours, those they in turn value, and so on,
Popeye"

i've had good results with all of these, you can use them almost interchangeably.