How many science points can be obtained through experiments in the whole solar system

I've found two potential solutions to this:

Minimize the Nav Ball - this prevents shift from activating the thrusters

Double-click to focus - If you can see an object, you can double click to focus on it.

So you're correct in using Jool for a gravitational slingshot into a high inclination, and you're also correct in assuming that you can only get about 40° from an encounter prior to switching the spheres of influence. Trying to set up burns prior to switching SoI is an exercise in futility. What you do want to do is set up your encounter so that you're coming in close to over a pole. 200m/s early (about a month out from switching SoI) can save a lot down the road.

Getting your trans-Joolian burn correct is actually one of the biggest factors for saving fuel. Not only do you minimize delta-V on the transfer burn, but you'll also minimize delta-V on the polar injection burn. You want to start your transfer about 65° after crossing the terminator into night when Jool is leading Kerbin by about 95°. When it comes to the phase angle, burning too early is really bad, as delta-V costs go up exponentially with the amount of time before optimal. Burning late isn't so bad, as costs go up much slower (quadratically maybe? Don't know for sure). This is a utility for determining optimal burn patterns.

So you've done your transfer burn, and you've done your final correction burn before switching SoI, and you're just waiting those last few seconds before that Jool orbit line changes from yellow to green. When that happens, you'll want to immediately plop down a maneuver node not too far in front of you. You're basically going to be doing a bunch of min-maxing to get your inclination into the high eighties. First, set your incoming inclination for best result inclination. Next, add about 500m/s of prograde velocity. You're doing this because you essentially have to kill something like 4000m/s of horizontal velocity and turn that into vertical. Next, reduce your periapse using the ground vector until optimal. Rinse and repeat, adding the most velocity in the prograde direction. Eventually, you'll get to a point where the inclination of the resulting orbit is correct, but the periapse will be in the sun, or the apoapse will be way out of the system. You're three options are to try and fix it now, try to fix it at Jool periapse, or (easily) fix it once you achieve polar orbit.

It's a tough operation, but with patience and experimentation, you should be able to get it every time.