Guillotined in Lock-down (Half-Guard)

Tuesday I was rolling no-gi with one of our purple belts named Thomas. We started rolling I pulled quarter-guard and instinctively held his leg from going no-hand-pass as always. Thomas is a skinny guy who loves to go for neck attacks. I got to my lockdown where he gave me double under-hooks. I then began to work for an old school but he got a chin strap wrap around my neck with his left hand (my lockdown is on his right leg, so chin strap on the opposite side of lockdown). He then began to quickly unhook my lockdown and get to quarter and then no hand pass and I was unable to prevent it because of the neck threat. After which he would finish the guillotine. This happened about 6 more times during the roll. At one point I even stopped rolling and went to get my phone to look up a solution but I could find none. Later that night I came to the conclusion that maybe I wasn't on my side enough and that I was too underneath him or that I wasn't low on his belly enough with my lockdown. I asked him to get it on me again and I asked him for help on how to prevent it and he said don't get the under-hook, but obviously, we need the under-hook in half guard.

I came up with one of my own solutions which involves grabbing the foot I have locked down with my opposite side hand behind his other legs hamstring, effectively forming a full guard with my hand and outside leg. This enabled me to pry out of his guillotine and even throw him off balance to the right so he couldn't wrap my neck.

Does anyone have any suggestions?