I felt like going for the assassin, as opposed to the regular arm across guillotine from guard, actually gave larger people greater leverage to peak out their head during the transition from front headlock to mount; this is likely because my choking arm elbow jutted off to the side rather than being directly under their chin, making my arm clamp weak. What's worse, my jutting elbow allowed my opponent to actually reach for my choking elbow and peel it to relieve the choke while putting an almost kimura like torque on my shoulder.
Even once in the assassin, the larger person was more difficult to finish with the classic guillotine hand grip, even with only mild resistance. I found more success finishing the choke when transferring the hand of my choking arm to the inside of my near side thigh. Keeping my hand on my inner thigh even seemed to help me turn them onto their back from FrH to the mount as well as protect my shoulder against the kimura-like torque that the opponent could put on my shoulder from peaking out.
Grips for front headlock chokes are as vagarious as drops in a storm. Not all are created equal though, of course.
You can try the deep tricep grip, like the one demonstrated by Ben Darmstatd above, or like shown here (besides the finish).
The inwardness would be greater positive control over how he turns, as well as keeping his arm in position to push his shoulder and neck together.
Another option would be what i call the power assist grip. It can be done open hand or closed fist, with arm in or no arm.
Melanson shows a no arm closed fist version here. Also known as the 'gogo choke' that Ben Rothwell used on Matt Mitrione and Josh Barnett.
An arm in version would be similar to the choke shown here vs half-guard, only with your other arm also going in deep to grip your wrist or your elbow to lock it in tight.
This is one of those things i've 'sat on' for a while, but i think sufficient time has passed (and enough people putting out similar materials) now that it's fine to share. The inwardness of it all is basically... when hitting a 'classic' guillotine, the idea is to push their head down into your hands/push your hands up into their neck. Well, as a demonstration, try putting your hands together in front of you and push them up; what is the most natural way of doing such a movement? Like a prayer position perhaps? Well, how about if you want to lock your arms together in some way, what then? The common grip of taking one hand and cupping under the other more or less doesn't go past horizontal 'naturally', and if you do you are pretty much working against your wrists; closing your elbows together basically pops the grip out.
What to do then? Well, really its simple; look at you holding your arm up in front of you (like if you were flipping someone off), and just... grip it like that. Around the wrist, or elbow, or tricep. You have the option of adjusting how deep you go to account for your angle of attack or how large or how small your target is. When done well, you can even potentially finish in just the head-to-head position by just slowly ratcheting up the pressure, without necessarily needing to go torso-to-torso (though, obviously, this multiplies your finishing power, torso-to-torso pinning their back on the ground most especially).