That's not been my experience at all in wrestling, hapkido, or BJJ. Case in point: the other big guy white belt that matches my intensity. He's also been going just a few months, like me.
If I was a grappling phenom (which I specifically denied by saying I'm not Kano), then I wouldn't be complaining about my white belt frustrations.
The phenom comment was in relation to you saying that you were not using brute force to make your technique work. For most people, it takes years to get to that point. Its something we constantly work on. When I run into someone who is too strong for a technique that I am applying... it means I need to figure out how to do the technique without relying on so much muscle. We often don't realize how much muscle we are using, until someone is strong enough to stop it. This is not binary, on or off... it is by degrees. As your understanding of the technique improves, the less you will be relying on muscle to use it... thus you will be able to apply to stronger people. Then you will find someone too strong, and you start the iteration again.
He shoots for a double leg. He leaves his neck exposed, so I go for the guillotine. He basically just shrugs it off and then takes me down. (I don't usually finish guillotines, but most folks at least have to fight their way out of it when I catch them). I land and get into half guard. I get my frames. Again, he basically just shrugs them off and grabs my arm to set up an Americana. He just bench presses my arm to flatten me out, and gets the submission.
So, we have learned that the guillotine won't work on him, in this situation. Try something new next time.
Don't forget your TKD. In TKD, if the other guy were to throw a spinning reverse round house kick... ideally you start your counter/defense as he starts his move. You can defend that attack, by simply moving the right way at the right time. Frustrate him enough and he will get sloppy or over extend.... Develop the same thing here. As he shoots, you should begin your defense, well before he ever makes contact. Change your angle, start your sprawl... move as he moves so that his take down attempt gets sloppy or over extended...
You got to his back.... thats progress. Thats great technique. Sure, you now have to learn not to leave your leg open... but, keep getting his back. It will force him to change how he goes about his take down. You may end up with your own opportunity....
I don't really have the opportunity to try and do something to him.
This is a mental thing. You always have the opportunity to do something, unless you are unconscious.
As soon as we connect, he basically has full control over where I'm going.
Only if you allow it. One of the funest ways to counter a double leg, is to let them have it. Go with it. Use all that energy to counter roll them, and end up on top. Sure, it takes timing and practice... but it sure is fun to get. If he is worried about that, it will slow his next attempt a bit.
The point is that you don't have to force him to go back... in order to control what is going on. He may take that direction away from you... but it leaves most other directions open... and if you can use his own strength, to help go where you want, it gets harder for him to resist.... it puts you in control.
If he gets his hands on my arms, he controls my arms. There is no in-between where I have an opportunity to defend.
This is the mental thing again. First... if he has grabbed your arms and is not letting go... he is not hitting you, and he is not choking you. He is not the only one attached to your arms.... you are on the other end.... and can have some influence. My sensei used to say, I have as much control over your arm as the strength of your grip.
If he is using strength to pin some part of you, use the other parts of you. Learning to move your body on the ground, underneath a bigger and stronger opponent takes time... but it is possible. (the art you are studying is famous for doing that) The first step is to not mentally accept that you can do nothing, or that he is in control. Don't fight against where he is applying strength... squish out the side...