I've gotten used to people asking questions like yours who have little to no competition experience but are more than willing to throw a lot of money at a car. My apologies...I've just gotten a little cynical/jaded lately.
Anyway, you would need one extremely exotic motor to get over 300 all-motor hp to the wheels from a B-series. Not to say that it can't be done, but I imagine that the power peak would be around 11,000 RPM. You could spend 13 grand on the spiffiest motor Importbuilders builds which is basically two liters with a ton of headwork, high CR, lumpy cams and individual throttle bodies. With an ITR intake manifold similar motors have hit 240 whp, but your guess is as good as mine on how much power the ITB's will add. I'm thinking the ITB's are good for maybe another 20-30 whp for a total of around 260 to the wheels. No, it's not 300-something whp, but in a 2100 lb car you've already matched the power/weight ratio of a Corvette Z06.
Now if you threw 13 grand at some sort of forced induction project, it would most assuredly top 300 whp. You'd have to tune the fuel pretty tightly but with that much of a budget I wouldn't be overly concerned about reliability. Any motor regardless of induction setup is perfectly able to blow up if it leans out and detonates.
On the weight issue, most of the weight you can remove from a CRX is in the engine compartment (the interior doesn't weigh much) by getting rid of the A/C and other miscellaneous stuff you might not need. Moving the battery to the passenger-side of the trunk helps the distribution out a bit as well.
I don't know how much money you want to spend, and forced induced Hondas aren't legal for most forms of road racing that I know of. Once you get into motor swapping and such you really do have to look at what you can and can't do for a given class.