I use the Gentleman combo as more of an interrupter than a real combo starter. Keep them on their toes. By no means is this a spammable move, but it's not punished as harshly as you say if you use it sparsely.
Nair>Dthrow is nice, but be slower on the approach afterward as just about every character that I've used the dthrow on, regardless of percent, is able to hit or airdodge before you can approach for a chain hit (i.e. uair). The best situation to approach immediately is if they pop up at a high angle above you, at which point you can use the FULL reach of your uair to chase combo immediately (beware airdodge though, as this loses you a valuable combo if they do dodge it. They'll generally hit the ground before you can get another uair off). That said, a pause after your dthrows will generally benefit you. Again, mix this up a little, mindgames are absolutely necessary for you to accomplish any comboing out of a throw in this game. Nair also works if they're at low percents and you wait briefly before the chase (short hop and immediate nair for both hits will sometimes work on taller characters here). I agree with Mann: play more aggressively. If he's afraid of being hit in the air, he just needs to wise up and learn how to coax you into missing your counterattack (airdodge, fast fall out of the way and followup with combo).
Your use of the dair is decent, as it looks like most of them are autocancelled, which makes it a fine approach as long as you're soaring past them in the process (i.e. land behind them with good distance).
Don't approach with the knee unless your opponent is mentally handicapped. You'll get shield grabbed without question.
Take advantage of the platform more. When he recovers and lands on the platform, you miss a lot of opportunities for uair combos or bair finishes. Falcon's priority lies directly above him. Abuse this.
If he's EVER above you and forced to drop down through a platform to attack, try to beat him to it with uair chains.
Good use of the utilt. I've found that working in the ftilt isn't too shabby either. Try to find a healthy way of mixing that in somehow. Variety helps massively with Falcon.
Also, you have plenty of opportunities to Raptor Boost, considering how you use it only rarely (actually, I don't recall you using it on the ground EVER in these matches, air yes though). Since you already use it rarely, using it to take an opponent by surprise at the 20%-40% range is good, as that is about the weight that puts them in comboable range. Unfortunately, higher percents toss them ridiculously high, making it difficult to lead into a combo that way. If you connect a Raptor Boost at that point, you'll have to mix in some mindgames to keep them in the air. Try empty shorthops, or hop and fastfall onto the platform. Any method of feinting works well here.
Mindgames. You guys need to incorporate them a little more. More feinting, baiting, reverse smashing, leading, etc. Both of you guys could use some overall improvements on this.
Work on edgeguarding. This speaks for itself, you guys aren't working each other off the ledge enough.
Obviously suicide less.
And that's all I can offer.
