Not how to beat him. Just how can I feel like rolling with him isn't a complete waste of time?
I've never beaten my professor or the purple belts at my gym. But I get so much out of those rolls because I'm able to at least do something with what they give me, and I'm able to learn something from rolling with them.
With this guy, I mainly see rolling with him as a waste of 5 minutes. It's time I'm not going to learn anything, not going to get to do much work, and just gonna get smashed and tapped over and over again.
Your suggestions are long-term suggestions about how to overcome him. While they are good suggestions, I'm more looking for short-term suggestions to overcome the frustration. Without going into too much detail, I've settled on #4. But accepting that he's going to smash me doesn't really make me see the point in just getting smashed for 5 minutes.
You're on the right track. Beating your partner isn't your immediate goal. Learning something is. So the question becomes, how can you learn something in your rolls with this particular training partner?
Jiu-jitsu is largely a game of positioning. If you are going up against someone who is bigger and stronger, then you can't afford to be in a position of equal leverage, because then they can match their strength directly against yours to force you into a position of inferior leverage and it just goes downhill from there. So at every step of your match, you are trying to improve your positioning relative to your partner. When he goes to square up with you, you work to establish an angle. If he grabs your wrist with a killer grip that you can't break, bring your elbow to your ribs to limit his ability to manipulate your arm. If you can't bring your elbow back to your body, move your body up to your elbow. And so on.
Of course, you say that his skill level matches yours, so he's trying to do all the same things to you. You work to establish a favorable angle on him, he adjusts to square up and then establish a favorable angle on you. On average, your skills will cancel out and then he'll be able to win using his superior physical attributes. That's fine, it doesn't prevent you from learning something from the match. Let's look at some possibilities...
If you're skills are even, then at least half the time you should be able to win a positional battle, at least momentarily. Perhaps you got to an angle on his side where he wasn't facing you and so he had to adjust and square up before progressing. That's great! When you review the sparring session afterwards, note that as something you did correctly and should do again next time.
Then think about what happened next. Why weren't you able to maintain that superior position?
Perhaps he squared back up with you, you got your angle again, then he squared up with you again and you gave it up as not working. That's an important lesson. Never stop fighting for that superior angle - especially against someone with superior physical attributes. You can't afford to give up on movement and become static.
Or perhaps he squared up with you and you tried to regain your angle, but he got some sort of grip on you which limited your movement and you couldn't get the position back. Okay, that's something else to learn. Unless he already has you in a perfectly set finishing pin, even a stronger opponent shouldn't be able to just grab you and completely shut down your movement. Try to figure out the correct movement to keep him from pinning you in place as he advanced his position. If you can't figure it out on your own, try asking your teacher. Or maybe your sparring partner himself might be able to offer some ideas.
Worst case scenario, your partner gets to a dominant position that you can't escape and starts hunting submissions. Now your job becomes survival. Figure out all the little adjustments you can make to make yourself difficult to submit and give yourself an opportunity to escape if he makes any mistakes. I have plenty of times been stuck underneath sparring partners of comparable skill and far superior strength. In those cases I've learned a lot of small adjustments to frustrate their ability to submit me. You can do the same.