I think the engineering bit is concerning making sure someone who is an engineer and qualified welder does the work and is insured. In truth any structural trailer modification that involves change to a standard production trailer possibly needs aengineeer to sign off on otherwise you may be left in insurance hell uncovered if something went wrong.
Sleeving just moves the stress point / flex point , spreads load sometimes and doesn't change the thickness of original metal and welds. That original drawbar may not be up to it longer term.
I've not seen ones with the hinged drawbar have cable brakes May be hard to keep adjusted and still have the hitch hinge?
Are you on cable steering? If you disconnected teh steering rod at teh motor would teh motor pivot sideways enough to get you in. Quite easy to use a pin and r clip instead of current set up and would take only seconds to do each time? Same if the motor have a permatrim - how much do you need teh permatrim?
I'm not a fan of cutting Gal trailers but at least if you have it done it won't be the end in the salt water.
From the photo it doesn't look like you can move the winch post forward and then more boat forward as it would also meand moving rear roller brackets and also axel forward. OK if it was all bolt on but I think Makay weld on suspension etc now?
I'd forget the hinge and simply put a small "v" block on the winch post and slide it back,, cut drawbar to a length that it would fit in shed, internal sleeve the existing drawbar and double horizontal through bolt it somewhere back under the winch post with high tensile bolts and locknuts.. Then do a outer sleeve with your hitch attached which could be held on by normal hayman reece style towbar pins. For a quick release of the brake cable you can buy rated stainless locking, quick release shackles that are used on yachts The inner sleeve it to ensure the hayman reece style pins pull on solid thick walled metal as your existing drawbar won't be real thick. An engineer would probably sign off on that as stressed components are off the shelf and no new welding of thin walled drawbar, and except for the one cut end of existing drawbar couple of holes and everything can be hot dipped..
Must love that shed more than ya trailer.