Kevin has some really good points about proprioception. I often relate that just as uke grabbing your wrist lets you know where they are, you grabbing your ukes arm lets them know where you are!
As far as a fully resisting uke is concerned (ie "I'm not going to bend my elbow") I would suggest you ask said uke to try a little experiment. As your uke to stand on the spot and tense all of their muscles - arms, legs, the lot. Then ask them to try and jump up and down. If they tense everything they won't be able to move.
Striking (punching, kicking, shuto, etc.) when you have a stiff arm is akin to trying to drive without bending your arms. You simply can't drive without bending/relaxing your arm. The uke that "straight arms" an attack is simply inviting a broken arm or a damaged elbow or again as Kevin mentioned a nice hip throw.
No one throws a punch and leaves the arm hanging out there trying to muscle their way out of something...
Back to your original question - I'm not 6' 2" so I can't comment on the height aspect, but having ducks disease at 5' 7" I often have people taller than me where I find myself in a similar situation. It often helps to remember that your ukes strike must come to you, not the other way around. When you can effectively meet, blend and control (not grab) the attack, you should be able to lower your centre over your ukes and draw them to the ground. This assumes that you keep unbendable arm not draw your uke into your own centre.
Its a challenging but fun technique to play with and you invariably get a different result every time you change uke (unless you're practiced enough to replicate the effect every time (one year I'll get this!)).
Hope the practice goes well