Try these changes. I play it along with the album and it sounds right.
The intro progression is somewhat different, but I think it's just an
E-A-B-A kind of thing. Let me know if you think this is better.

Liz Myers

EE Piano Chord 

You told me tales of love and glory
AA Piano Chord 

Same old sad song, same old story
EE Piano Chord 
             C#mC#m Piano Chord 

Sirens sing a lullaby
G#mG#m Piano Chord 
              BB Piano Chord 

And no one knows but Lorelei

Castles out of fairy tales
Timbers shiver where once there sailed
A lovesick man who caught her eye
And no one knew but Lorelei

F#mF#m Piano Chord 

CHORUS: River, river have mercy
BB Piano Chord 

Take me down to the sea
F#mF#m Piano Chord 

For if I perish on these rocks
BB Piano Chord 

My love no more I'll see

I've thought of you in far-off places
Puzzled over lipstick traces
So help me God, I will not try
And then I think of Lorelei
I've traveled far and wandered wide
An old photograph of you beside me
Old Man River seems so shy (?)
And he remembers Lorelei

CHORUS

If I should float upon this stream
And see you in my madman's dream
I'd sink into your troubled eyes
And none would know save Lorelei

CHORUS: Oh, river river river have mercy...

But if my ship which sails tomorrow
Should crash against these rocks, my sorrows
I will drown, before I die
It's you I'll see, not Lorelei
EE Piano Chord 

I-I-I

Outro: E A2 (repeat & end on E)