I've done this before, and it's extremely tedious...there's several how-to articles on Modelwarships.com that would make life alot easier...
That being said...balsa is too soft and has too coarse of a grain for 1/350.
I would suggest using gumwood, or some other tight grain wood. There are several companies that do veneers in the dimensions you'll require, but it's going to cost more than the kit and PE combined.
Replacing the plastic deck with a thinner sheet, then laminating that, is one way to go...this insures you're not cutting around fittings, etc. I'd strongly suggest using plastic sheet, and keeping the original kit parts intact, for several reasons. First would be to reference the fittings, the second would be 'just in case' the project becomes too much, you can always fall back on the plastic decks.
Regards,
Jeff Herne
Modelwarships.com