You seem to also feel as though you were obligated to land no matter what was going on.
Actually, you hit the nail on the head here. Working with instructors around this particular airport for years, I was brought up to feel that any slip-up at this particular tower, and I could expect to lose my license and be fined out of existence. I will say, I did feel a particular NEED to land on the first go.
Before continuing, I want to state that when I read your debrief, I saw it as instruction offered, not as an attack or anything, so please do not read this as argument, or rebuttal.
The idea of a go-around actually entered into my mind just as I leveled out and regained control. Three things jumped into my head: Despite having had good results from removing the glasses, I wasn't positive that was the cause of the loss of control; The landing wouldn't be as perfect as I would have liked, I knew with a little finesse, I could make it; and third, I was shaken up. The safest thing for me to do was get on the ground while I was still thinking clearly.
Even after landing, I wasn't convinced the glasses were the sole root of the problem, I'm still not. The way the controls seized just didn't seem right for interference with the stick, so I just wanted to hit the dirt, ASAP. In retrospect, that is not good motivation to go to ground. That would imply I would land even if I would miss the LAHSO. That's not the case, but I won't lie, my ADM wasn't perfect, and I was shaken.
There were two key factors to deciding to try to stick the landing. Firstly, I was fast, but low. As I saw it, my extra speed at that point in my approach was compensated for by my lack of altitude at that point in the approach. Secondly, I felt I would be able to determine several more seconds into the approach whether I could absolutely make it, or not. And with my power-to-weight ratio and climb rate, so even if I touched down, and just could not apply brakes fast enough, I knew I could throttle up and get back above pattern altitude in MUCH less time than it would take to continue slowing down.
Long story short, shaken and unsure, the one thing I knew was that I was confident I could make the landing, and that if it ever got too close for comfort, I could get back into the air without violating the LAHSO.
Perhaps it was the wrong decision. As a third party observer, I know I would be questioning my own decision right now. Had the altitude or speed been even the slightest bit different, I may have made a different decision. And I was CERTAINLY wrong to have felt constrained to land. But that was my thought process.
Both your post and mine however, go a LONG way to emphasizing the need for instruction BEFORE climbing into ANY cockpit!