Richard,
The Z car is an incredible car and one of the key things is the suspension and handling is part of the key to it's successful racing heritage. You can build them into big HP supercars but as others have said the cost is often much more in time and money than typical American cars but in the end you get a car that will kick their ass on a road course and street. To me it is a waste to turn a super handling car into a solid axel car that handles like crap.
You can use your welding skills as the rear quarters and the top and bottom of the front windshield were lead welded. This is a non frame car so it is unibody design so for big HP you could use your welding skills to eliminate the lead and make those seams strong. Also I have added custom frame rails to make the chassis strong that looks like stock from a far but to a more in the know Z owner you notice that is has been modified. That is where your welding will definitely be valuable as that requires a lot of welding. There are good kits from Arizona Z car and Techno Toys that changes the rear end mounts to handle Q45 and other stronger rear ends for big HP and if you go crazy then you might either add to those cryogenic treatments or go for big bucks and go for Jerico and other road race rear ends. You DO NOT want to loose four wheel independent suspension of the Z so the bigger the HP the more the costs can scare you but it will be worth it.
You do not need to go that high of an HP to get these cars to out perform many others. HP in the 300-450 will be very quick on a car that is so light. Sure you can build them for 700 to 1000 HP but you better have the money to build it right so you keep the car a great handling machine and if you go with that HP these cars will be one of the fastest on the street and able to beat most super cars.
FYI, I own the Primadonna Z car as well as two other Z cars. I have a more street 240Z with a 3 liter Datsun Spirit engine, coil overs, etc. that is pretty darn quick and handles like it is on rails and that did not need 700 HP but more like the 300's. Also most Z cars do not have the aero dynamics to fully use over 700 unless you do even more body mods. The Primadonna is stable at high speeds and will be back on the street eventually with a 750-1000 HP RIPS racing straight 6 and will be ready to take down most supercars but it will take some years as that build is not for the faint of heart...as that will be a over 200 mph street storming monster