Sometimes orchestras contain less than 8 first violins; this is a mistake, as the balance between strings and wind is completely destroyed.
This book seems to be intended for writing to larger orchestras used in romantic era.
I'm mainly concerned about the small number of strings. I'd really appreciate some tips how one should handle that small string section and if someone could point out some web page or book about writing to that small orchestra.
Broadway pit orchestras get away with much smaller string sections than this and emulate all sorts of styles, from every imaginable period. I'd recommend listening to the cast albums for some of the old shows, with full pit orchestras, to see how their orchestrators arranged the score. One particular show comes to mind immediately -- "On Your Toes" -- because it has to suggest a ballet orchestra for quite a few numbers.
Another way to look at it is like this. You could half the number of players on the list you referenced and have an orchestra the size of one used in most of Sondheim's shows (many of which have a "classical" flavor.)
Still another take would be to reduce the number of woodwind players by half, use one percussionist and one trumpet, but keep your string section as is, so that it sounds proportionally larger.
I am a novice as an orchestrator as well as a composer, but I am a professional actor and I have a lot of contact with the NY theater scene, and I get to hear a lot of innovative scores. My impression is that a top notch orchestrator can do a great job with whatever instruments are available.