Red October Submarine Conversion

I can't remember the last ship I built but I thought I'd try the Red October from Tom Clancy's book. 

According to the book the boat is both longer and has a broader beam than the standard Typhoon (Revell's kit).  I need to cut the hull from stem to stern and add some sheet plastic to increase the beam. Is there a technique I can use to make the cut perfectly straight?  The hull is split into a top and a bottom. Mitre boxes are obviously not a choice since I need to make the cut in a different direction than the box will allow.

Also, would it be better to cut the top and bottom seperately or glue the hull halves together and cut both at once?

TIA.