You're right, body press cross up is most defenately a dizzy nightmare...I knew I was forgetting shit, I honestly tried to cover everything I remembered at the time, but damn I forgot one very important deal there...well, I hope he gets it all!
Before I forget I wanted to add that footsies are a thing that Zangief will always win at, 'cause his pile driver has more reach than people think, specially when they want to poke you, the instant you see (usually a middle kick) a poke started you do your pile driver and you'll catch 'em. You might say that the pile driver can reach about the space of another body between you and the opponent, sometimes even more depending on the oponent.
Good footsies players like Fei long, Cammy and so on will try to keep you away with their quick medium reach attacks, you got to remember above all that Zangief can take a lot of heat, so as long as you don't loose your cool if you're trapped in a cross up or a frontal combo you wouldn't be doing what the opponent expect thus your retaliation will be swift and surprising.
Be weary of Dhalsim as you are trying to learn to play with Zangief he will cost you a bit of work to get near him, patience here pays in fold, as you can close in inch by inch until you make him make mistakes and then you go for the kill. Good Zangief players know that Dhalsim is not an issue, but for now know that you need to pay close attention to this type of match. Keeping the pressure is the key to victory for Zangief and it still doesn't change in this case, you just gotta learn how to keep the pressure from afar in order to close in.
I also noticed that I madea typo in this
Practice your weak up pile driver and atomic buster, it could save your ass plenty of times
I meant
wake up, it makes a world of difference so sorry about that.
I'm sure I'm forgetting more stuff, but I'm sure you'll find you're own tricks as the game is so versatile is not even funny, that's why SSF2T is my favorite Capcom game ever, this HD remix game is just such a gift for me, in my opinion they couldn't have done any better.