I added a few more . Are they helpful ? Trying to avoid buying a truck to use just to tow boat .
The photos are very helpful. Your trailer is pushing the limits of "minimum sizing" in my mind, but I'm conservative on such things. However, all is not lost.
Remember, even if you had a huge trailer, you can't simply move the boat back to get a light tongue weight. A tongue weight too light will make any trailer sway like a hooker advertising for business. So, there is a limit you will reach where the rig will become unstable. In the extreme, it can even flip the trailer, or cause you to jack-knife the vehicle/trailer. The risk of trailer sway is usually the highest at higher speeds; if a trailer sways, slowing down usually results in the sway subsiding.
I'm hesitant to tell you to hang the transom off the back of the trailer bunks, but that can be dealt with. As I said, there's a limit to how much you can move based on looking at the winch stand. Measure that, with allowance to keep the tongue jack on there, just move it back also. Let's say that results in room to move the winch stand back another 5-6 inches. You might not be able to tow like that, but that's the adjustment room you can muster up front.
Now to fix the back. Notice that the bunk boards are held on with right angle brackets. The bracket will be screwed into the bottom of the bunk board. You would want to move those brackets forward on the bunk board so that the new position of the bunk board puts it back far enough so that the transom rests on it - when you've moved the winch stand back. As an example, 6 inches + 4 inches (current overhang) means you move the brackets forward 10 inches. Moving those forward will move the board to the rear, again supporting the transom. You can even buy longer bunk boards already covered with carpet if you like that idea.
You can try moving the boat as described, but that's not to say the tongue weight will still be adequate. You'll need to tow it to find out. You really should keep a good weight there; 100# may be too light, but you might get away with 200#. It's hard to tell since you have no idea what the tongue weight is now.