I had the same problem. Here is my solution. It does not involve changing the stock messenger and gives MUCH more flexibility in vibration pattern, which is one of main reasons we are on Android, no? Of course Google should have this in their stock Android, but I won't wait for that if I can customize my experience now......
Here is my solution :
Step 1 (controlling vibration pattern):
I suggest downloading "Good vibrations" app. Then go to "good vibrations" - On Main tab, click "enable application". Then go down to SMS pattern (click top left settings tab to get there) and click "enable custom SMS pattern" and the pick a custom SMS pattern on bottom. I chose "2 x 400 (pause 125)", which seems to approximate the "2 vibrations" I had before. You can find similar apps if you type "text vibrations" in Google play, but I found this one to work best. *NOTE* You need to turn off stock app vibration - go to stock messenger app, click settings and go to "notifications" and uncheck vibrate (leave everything else same). (edit: you could also make repeat message alert to "never", but keep "notifications" "Green button on top" ON and keep "Preview Message" checked if you want to keep receiving TEXT alert on your lock screen).
Step 2 (repeating vibration, if desired):
In case I am busy and miss the first vibration, I like it to repeat. I don't think the stock messenger "repeating function" in the settings works. I have used the following app in past and it still works well. I suggest downloading "Easy Reminder". Just go into app and enable "Remind SMS/MMS" and click that option. Click "remind SMS". Select your "timeout" value (e.g. I selected 2m so that it will vibrate every 2 minutes until it stops). Check the "vibrate button". Then go to "repeat times" (I selected 10, so that it will repeat vibration every 2 minutes for 10 times). (edit: if you want sound alert for texts when you're not in vibrate mode on your phone, just add the sound you want under "sound" as well)
3) I also use "Calendar Snooze" application to do same for my calendar reminder vibrations. Very customizable, love it.
Hope this helps.
Best,
Gus