First, here's a picture of my trailer. People have done wider bunks than these. So by all means, take that as a minimum. They extend nearly to the transom when the boat is loaded.

The picture also shows how I position the trailer so the rear-most roller is just at the water level, so it can grab the bow in the notch it has (that detail becomes visible in this photo if you click on it to enlarge the view). That roller is also 1-3" below the "level" made by the other rollers which helps transition the rear of the bot onto the bunks during retrieval, as the bunks will begin to "lift" the boat off that roller earlier. It also means that roller will not bear any weight in storage.
Now, to launch onto the hard: I place a bit of carpet where the hull will end up. Then I tilt the trailer until the boat starts to move. Usually the transom contacts the ground pretty immediately, at which point I pull the trailer forward. The bow will descend while rolling on the various rollers, until the trailer is out from under it. With a trailer that lacks the tilt feature you might need to disconnect the trailer so you can tilt it as a whole and somehow manually pull the trailer out.
Retrieval: I find that I need to limit the amount of tilt, so I lash an old rope around the trailer tongue to let it still tilt some, but not the full steep angle (if the angle is too steep, the bow will "dig in" between rollers). I roll the trailer so the rearmost roller touches the bow, connect the winch and put a bit of tension on it. Then I support the bow going up that roller. With help of a block of wood or two, I can manage that process by myself. Once the bow is on a roller, I simply winch the trailer under the boat. I connect it to the car only after the boat is loaded. (I imagine this would work pretty much the same for a non-tilting trailer).
Hope this helps. (If you want to discuss your repair, please make a new topic for that).