Have you ever tried Mystic Ray or Hidden Missiles with Wright? I was thinking about a Wright team of Shuma-Gorath / Wright / Taskmaster. Shuma-Gorath can TAC glitch Wright in.
In all honesty I don't really think Shuma-Gorath goes to well with Wright. Don't get me wrong a full screen beam assist is great for Wright and buys him a little time to get situated. Other than that though I don't see too much synergy going on. In all of my Wright time I have learned to not rely on Air Exchange Objections only. Your opponent will expect it and just wait for you to switch your character and open up your incomming character easily.
As for Taskmaster I have breifly tried him on my team in replacement of Wesker. While Tasky is most defenitly effective in assits and DHC synergy I still prefer other characters. He definitively does help. I don't like the reduced damage I was getting though without the OTG assist.
The only other thing I think Wright needs other than a get off me assist is a low hitting assit. When Wright is in Tournabout mode the man has little to no mix ups. But when you add an assit like Weskers gun shot into the mix it can be very hard to block the low hit and a jumping finger point.
Characters IMO that work well with Wright
Dante: Jam Sessions is the best assist for Wright. Covers to the top of the screen and also equals as a great get off me while buying a good chunk of time to grab evidence. Dante also DHC's wonderfully for Wright in almost any situation. Another awesome thing is during a team hyper combo Dante's million dollars buys enogh time to gather three or four pieces of evidence and wave dash up to land an Objection before the hyper ends.
Hulk: This is my preferred choice. Hulk anti air assist is a great defensive tool. Like you said though it does not open up for combos but it does it through a lot of moves and some hypers. This assist always buys enough time for a single piece of evidence. Since the assist is also pretty fast in recovery. It is possible to throw out Hulk and while the opponent is blocking or being hit throw out Maya shield by the time the shield is up and about to be drained you can throw another Hulk assist in and repeat the process. This wall is very hard to penetrate. Also Hulk IMO has great synergy with wright. Gamma crush into Maya hyper lands for some great damage and an easy Objection. Hulks alpha counter is also great in getting Wright out as it has a good amount of invincibility to it. It also always helps to have a high health character when maining Wright because he can get hit pretty bad.
I also think Wright works wonders for Hulk too. Missile assist is hulks best friend. He is a full screen low hitting attack that sets up for easy unblockables with Hulks attacks. Missile also lets Hulk combo after a command grab. Command grab throw out Missile then Gamma Charge H and launch. Break the witness is good too if you can pin the opponent down but that is kinda hard to do with Hulk.
Haggar: Lariat. Works wonders. Great defensive tool and even better lands brain dead objections. Good DHC synergy too.
Doom: Hidden Missiles lol
Wesker: Gun shot works great in extending combos and giving Wright some mix up potential he so desperately needs. Wright can't do that much damage in investigation mode but an OTG assist makes it respectable. Not much else really going for him other than that but I think the quick hitting low hit makes Wesker worth it.
She Hulk: I don't use her but I know a lot of people have tried this pairing with decent results. OTG definitely helps I'm sure. Theres probably some decent synergy too.
Frank: Shopping cart is great. High durability and pushes the opponent away. There's some pretty good synergy to boot to in DHC and what not. I haven't played with them that much because I don't think it's a good idea to have two power up characters on the same team.
Thats my two cents on character team ideas. I run Wright/Hulk/Wesker. I always preferred Wright as a on point character. I totally get why people put him second. I do. Safer start and using DHC's to bring him in and get evidence. I also think that if you can't get evidence using basic wright and knowing when and not to search for it is key. If you can't use Investigation Wright and do anything whats going to stop your opponent from just snapping you in and taking you out in a milla second. I know my team isn't perfect there are some definite flaws. Good Vergils, Dormammus, Hawkeye and Zoning teams can eat me alive. But if I can't deal with that then it's already game over.
Dear God I typed way too much without noticing. LOL