Any more details then a flat bottom 16ft boat? Maker unknown? In a formerly no titles for boats so it never had 1, now it's registered as a home built? Any more pix, possibly showing the interior of the boat from above, the outside shape of the transom and the profile of the entire boat. Flat bottom jon boat w/ the flat bow, a slight semi-vee w/ very little V, mostly flat? Welded aluminum boat (based on the corner gussets or riveted boat? HEAVY gauge vintage aluminum boat, or lighter weight/thin gauge aluminum?
Knowing some of that ^^^ will help determine what to do about this:
The 3 2x4 'knee' braces are NOT original, the 2 painted white probably are. Based on that pix ^^^ I suspect 2 things:
The current transom is NOT original, AND it's not adequately supporting the torque of a 55hp motor.
I haven't seen every old aluminum boat made, but I've seen a bunch, and I doubt that the original layout of the 2 metal knee braces was done so that they WEREN'T fully in contact w/ the transom plywood. Following that logic, it sounds to me like the torque of the motor is putting pressure against the bottom edge of the piece of plywood, and w/out enough vertical surface area of the knee brace foot in contact with the plywood, it's allowing the aluminum skin to flex inward below the transom plywood, if only slightly. The pix isn't really clear, but it also appears that the 2X4's are only in contact w/ the transom plywood across an also very small cross section.
W/out more info about the actual boat, I won't hazard a guess as to whether the 55hp is in excess of the boat's actual hp rating, but it's clearly in excess of the current setup of the boat & it's transom.
I'm not sure full cover transom is the correct use or term, WOG, but I completely agree: transom plywood that more fully covers the interior side of the transom skin would, IMO, certainly help resolve the current problem of the aluminum flexing. It wouldn't have to extend all the way to the inside corner of the transom/hull bottom, but certainly could extend further down the aluminum transom skin's height.
By the way, the knee braces may also be transferring the flex from the transom down thru to the bottom of the boat's hull. Constant movement of the aluminum hull, in about the same place regularly over time isn't good. IMO, it's extremely NOT GOOD. I'd remove the motor, existing transom plywood & existing knee braces and extremely carefully examine the transom skin & hull bottom. If those braces tie into stringers, how do they tie in, and is that attachment substantial enough.
Repeated flexing of the hull against a brace, stringer, rib, or rivet can lead to fairly minor or very major cracks in any of the components. We see LOTS of rib end, rivet hole & hull cracks in the Starcraft rebuilds. Many are so minor to have been indetectable until the boat was completely stripped of it's interior and the exterior hull had all traces of paint & primer removed.
Minor cracks tend to become larger over time & much more difficult to repair.
So, who made your boat & lets see some more pix of her