A few clarifying questions.
- Does the drummer use earplugs during practice? (If he does, that might make dynamics harder for him - he may not realize his own volume.)
- Does he have a kit to practice with outside of the rehearsal space?
It's not the ideal situation, but if he's willing to do it, you can do sectionals with him, one-on-one, with a metronome and something to record with. Record your rehearsals, listen to them, and then try to drill the weak points if you can.
Another thing that you can do, since he's open to using a click - record everyone's parts to a click, and let him practice against that at home if he has a kit. It will likely be harder for him to rush or drag a full recording than just a click and it should make any issues more obvious to him.
However - as others have said - you will just have to be patient. Improvement may come, but it won't come fast. You can help to speed it up by doing sections with him and taking more control of the rhythm section, but it will take time. Drums are physically demanding and the learning curve of bodily coordination, tempo, and meter can be pretty difficult. If he isn't practicing outside of rehearsals with the full band, he needs to be, or improvement won't happen.