Okay, guys. I was going to wait until I had an answer for every character. However, I have ways to cheese most of the characters in Hard survival. Unfortunately, I have never gotten past 41 Ryu, as he is a character I can't find a real answer for... Still, hopefully this info will help some other people get further and hopefully we can figure out some ways to beat some of the characters I don't have answers for. I made most of my attempts with R. Mika. However, I tried with a few other characters and this stuff seems to work with other characters.
If you jump back into the corner and just keep hammering a heavy attack some characters will walk into it, allowing for a free combo. After you finish the combo get back into the corner, rinse and repeat. A number of characters fall for this method. including...
Karin
She is the BEST character to gain health against. She will absolutely walk under you and allow you to land the neutral heavy attack. Rinse and repeat.
Dhalsim
Neutral jump fierce in the corner works well, but in a wonky way. He will sit back, spitting fire, for a lot of the round (just hop over it). Eventually he will teleport under you. This is when you bop him. He may tag you occasionally, but I wouldn’t be too concerned. I haven’t had him take more than a quarter of my health.
Necalli
Also an easy win, but will use his DP if you let him get right under you. Still, you should win without taking much damage.
Chun-Li
Not as effective as you would hope. She can mess you up, but it works fairly well most of the time. She will likely tag you with a few anti-airs. If you have less than half health going into this one it could go either way.
Laura
Similar to Necalli in that she is weak to the neutral jump heavy approach, but she will occasionally tag you with her DP grab (she can't follow it up for real damage, so don't sweat it). Stick to the plan, you should be able to walk away with the win.
Birdie
He has every tool in the world to deal with the strategy… but he won’t use them. Jump back fierce destroys him.
*Don't try this with anyone else not listed here; they will blow you up.*
Fang can be destroyed by just jumping at him aggressively. If he doesn't get a chance to breath he doesn't fight back. This can also work with Zangief, but occasionally he decides to anti-air and he will take half of your health with a crush-counter.
Another way to deal with Cammy and Zangief easily is to wait for them to walk forward and trip them. They eat the trip WAY more than not. This works a little on Vega, but it isn't nearly as consistent.
This next one is R. Mika specific... A way to take down R. Mika and Ken with R. Mika is to just space her HP Shooting Peach; they will continually walk into it.
As for Bison, Ryu, and Nash... I have no idea. Cross Ups work reasonably well on these characters to a certain extent. However, they all hit for crazy damage. I just can't seem to fight them without screwing up at some point and losing all the progress.
I hope this information is able to help someone. I hate this stupid mode.