He only needs one tweak. Lariat needs a better start up hit box to allow it to combo more consistently. If we could combo into lariat at any distance where c.lp-s.lk hits (and on crouching opponents too), we could put the fear into opponents trying to rush Gief down. Without that, most 4 frame punishes end up as just shy of 60 damage, with it they would be around 120.
If they did this, then it would mean that the opponent would have a 50/50 to defend against every time they make a bad decision close up. If they block they get grabbed (or a jab short hit confirm), if they jump they get hit, if they back dash they get hit, if they poke, they get hit, and if they invincible reversal they run the risk of being baited and crush countered. At the moment jumping is the best option because at worst they get air SPD'd (which requires a read and spot on execution) but will more than likely get jabbed into a reset or catch a whiffed spd.
As it stands he is low tier, if not 16th on the tier list, but I stand by my earlier point that learning Gief forces you to learn the game. You're not going to win with him by mindlessly crossing up or spamming reversals. Instead, you need to study the match ups, spot the holes and maximise your damage.
I agree that staying on top of him is a solid strategy as he no longer can grab you with a 2 frame spd, but with solid blocking and anti airs you can shut down most offence and force a mistake. It's capitalising on those mistakes that will make or break you as a Gief player, and will require hours of practice.
I'm also starting to suspect that Gief is similar to Birdie and Necali in that your early round should be spent building v trigger and meter, whilst slowly pushing your opponent to the corner with the intention of activating trigger at the earliest opportunity. You can combo into his super from pretty much every normal (I'm not sure if there are some I'm just not doing properly), and when in V Trigger you can combo into cyclone from most moves as well as parry multi hitting moves, all of which make him very scary to mess up against. It'll require more thought as to the best way of implementing this approach though. Being so meter dependent could end up being another reason for him being so low on the tier list.