Looking at things from TIM's perspective, he had two choices if he wanted to stop the Reapers. He could work with the Alliance on the Crucible project, but nobody knows what that is or how it works. It could backfire, or just plain not work at all. It's a galactic Hail Mary born out of desperation with absolutely no guarantee of success. Meanwhile, Henry Lawson's lab is achieving promising results in controlling Reaper tech, and given more time there is a chance that they can scale that up to take control of actual Reapers. It's a desperate hope too, but at least there's actual science going into the project and not wishes and prayers. Knowing what TIM knows, it makes sense that he would pursue the option of control.
Plus TIM seems to be looking beyond the war with the Reapers and how useful control of their technology would be to securing human dominance of the galaxy, so thats another reason controlling them probably appealed to him, heck thats probably the tract the Reapers used while indoctrinating him.