Escaping Sidemount Against a Larger Grappler 

But wouldn't you get in his guard then?

He’s holding himself back. Using strength all the while won’t teach him any technique. Try training with people a little smaller until your escape is better. I’m 6’3” and around 225, I have no shame in asking better sparring partners to teach me escapes to stuff they constantly catch me with. If he’s just a bit of a dick then you might just have to avoid him.

Try to frame with your elbows, not your hands

Sounds like that guy has a bad attitude, I realise your comment is 3 years old at this point but I would have suggested training with someone who has more flow and come back to aggressive types when you're more comfortable escaping from those positions. That being said, in Judo, I find people have insane top-pressure and if they get you in a good pin like kami shiho gatame (north south) you're pretty much stuck unless they're significantly lighter than you, so I've always been told that "the best escape from a pin is to avoid being pinned in the first place". I'm curious though, how are you finding your escapes these days, and are you still training?

+Vladimir Makhovskiy, I guess you need more practice. I have had the same problem with each movement, you need to know 100% the movement to make it without thinking, then you will be enough fast.