I use Handcent and so do not have the issues you have and have, in my opinion, a better SMS app.
I do not use MissedCall to handle SMS, but see that it can, so you would have to investigate that aspect yourself. Just letting you know there is another option out there. AND, btw, that app could also be configured to give you alerts for Calendar events, Missed call LED notification and sound as well as SMS.. so, it has more than 1 use.
/** SGS3 (rooted & stock ROM) **/
/** Asus Prime TF201 (rooted & mildly OC'd) BRICKED BY THE ASUS OTA JB UPATE!**/
/** OG Droid (rooted & OC'd & all hacked up) **/