It looks like your internal handle has an offset thumb latch. If so, take a look at the 82-030B keyed version of this handle set.
I'm sorry to hear that you're having trouble but I'm not quite sure what you mean by the lock housing not being large enough. If you mean that there is not enough space for the key lock to install in the door, it is sometimes necessary to enlarge the cutout in the door frame using something like a file until there is enough space for a lock body. If not, please get back to us with a detailed description of the problem you're experiencing and we'll do our best to assist you.
I do see what you mean but there is not a thicker version of this handle that would cover the entire key lock, unfortunately. The best workaround for this situation, which we come across from time to time, would be to carefully file the cutout out in the door where the lock inserts a little bit at a time. As long as you stop filing once the cutout is the appropriate size, there would be no reason for the lock to move while installed.
Also, keep in mind that the key lock comes with a long spindle that can be cut down to size to engage with the mortise lock. It is important to cut off a little bit at a time and test it if there is no original lock to match the spindle size. If too much is cut off, it will not engage the mortise lock. The process is shown at time stamp 3:25 in the video below.
Great! We'll be here if you have any other questions.
