Ok, if you are not connected to xbox live when you earn an achievement that achievement is stored on your local box.
If you then go and recover your gamer tag to a new box, the new box (and live.xbox.com) won't show those achievements. To have your achievements unified across all media you need to sign the box that earned them back into xbox live on that account.
Recovering your gamertag is a special processes where your gamertag is transfered to a new box and retroactively removed from all other boxes. Because you removed it from his old xbox before updating that achievements, you necessarily lost your ability to update those achievement.
I'm sorry, but you should always connect to xbox live whenever possible if you want to maintain your achievements. God forbid your box red rings and you lose all your work.
I'm not sure as to why exactly you're having issues, but I play Modern Warfare 3 on Xbox Live daily, and I've never had problems.
Occasionally there are server issues, but it's been surprisingly stable since launch as far as that's been concerned. If there's few players in the region/game type you select, sometimes the search times out, but generally you should then be placed in a lobby for other people to join you.
Is the game complaining about your NAT type? You want your NAT type to be open. If it is Strict or Moderate, you can usually change settings on your router to fix this issue.
If your network is properly configured, and you're logged into Xbox Live successfully, make sure you're not doing anything else on your internet connection, such as Netflix streaming or downloading/uploading large files. This can negatively impact your latency and cause you issues when you're trying to find a game.
Beyond these things, there's no "patch" to the game in the works or otherwise available to change the network settings the game uses.
Best Answer
The answer is maybe... If you have loaded your save on a different Xbox then yes you can. If you access the 2nd Xbox and load your save offline or choose the older save when online, you can overwrite the corrupted save and recover your game pre 7.37 update, though the save file will be whenever you logged onto Ark on the second Xbox.