Since you are talking about 15 hp, you can add a 5" extension to your transom....BTDT. You can build up some quality plywood to the thickness required to match the current transom and cover it with sheet aluminum or if in fresh water, galvanized steel...probably easier to get....AC duct work fab shops a source. Use a single piece making an inverted U shape, as many layers as you want to get the thickness you want, through bolt it to the old and new wood with 3M 5200 sealer on the bolts.
Mount the engine and with a helper, engine down in the run position, pointed straight ahead, take your foot and put down pressure on the AV plate of the engine and check for rigidity. If ok, fine. If not add an additional transom brace between the engine clamps on the extension.
If you do it right you will also reduce your "water over the transom" that has always been a problem with tiller operated, one person boats with 15" transoms as it will have 20" to climb before coming in the boat.
A fabricated "splash well " type bracket attached all the way across the transom would be a super brace and would/could provide extra splash protection too....just leave a place for any captured water to drain back out.