The canopy is built into the model, not painted on, so a quick fix isn't possible.
The recessed view is a nod to the stock Fed fighter (the Wraith class as some call it), which also has it's cockpit hidden behind the forward hull.
Replacing the canopy with a hull-door just wouldn't look right, so I left it as-is to provide a sense of familiarity and a quick access point for the pilot. From what I've seen, Starfleet is heavily reliant on technology anyway so having automation, tractor-beam landings and computer assisted maneuvering would be standard for their way of thinking.
Besides, starships themselves don't have windows on the bridge for tactical uses, just a big holographic screen that's fed data from sensors all over the ship. If any of those systems are offline, I doubt anybody is going to run to the front window and start spouting targeting range info to Mr. Chekov; what they are gonna do is shout at Scotty to hurry up and fix it while Kirk stalls the enemy for repair time.
Not that it matters as how often have we ever seen the viewscreen fail, despite the ship suffering catastrophic damage? If they've managed to master super-reliability for a tv set, I think a fighter HUD wouldn't be that far behind. Sure the HUD could fail, but just as easily could the phasers and I doubt anyone would suggest installing a GE MiniGun into the fighter for extra redundancy.
As for the position of the drive, who's to say the bulk of the engine isn't in the front of the hull, like a modern car, with just the exhaust port mounted aft? There's a reason the warp drive wasn't built-in, afterall.