Is EKE attackable by a brute-force password search?
Doing EKE over an EC group is a tricky (and is something that RFC6124 avoids).  The problem, as you note, is preventing an attacker from being able to determine whether a possible decryption is impossible (and hence he can remove that potential password from the list); that turns about to be considerably more involved than you would expect.

Even if you skip the first six bytes, well, the EC X and Y coordinates are not actually randomized (even though they look random); these coordinates are actually integers (if you're doing even-characteristic EC, field elements, don't worry about the distinction) which are related by an equation (perhaps $y^2 + ax = x^3 + b \mod p$) that's easy to check; this would easily allow an attacker to do a dictionary attack.

Now, all this can be handled; you can just use the X coordinate (ECDH still works just fine; however, your ECDH package might not support that), and you can deal with the problem that about half of the bit patterns are not possible EC X coordinates (and that's also easy to check); you could modify the encryption algorithm to deal with that as well.

On the other hand, all this is rather tricky for someone who isn't used to working with Elliptic Curves.  I would strongly recommend that you use either EKE using a MODP group (as RFC6124 has; don't forget you have you use the nonstandard generators that RFC6124 has), or go with SRP.