What is the best way to approach train tracks?
Firstly I would say that you should always ride in a way that is safe for you. If drivers have to wait as you take the necessary care, then so be it. They would have to wait hours if you fell and were killed. The only person taking responsibility for your safety is you.

Here in Melbourne (Australia), in addition to train tracks, we have tram tracks.



Rails tracks usually cross the road at angles from 90° to 30°. But tram tracks run along the roads, and also cross at various angles. Everybody falls at least once on the tram tracks, after allowing the front wheel to drop into the slot.

Danger

The danger is not just an embarrassing fall. Other traffic can hit you as you are suddenly launched sideways, under their wheels with fatal results. Less severe is if the wheel get caught in the slot, resulting in a buckled wheel.

If the tracks cause, as you say, jarring, then there is a risk that you can loose control. So slow down. Just assertively signal your intentions to surrounding traffic, and do what you need to do. If you travel the same route at regular times, the other drivers will get used to seeing you. 

The main risk to your bike in my experience is pinch flats. So keep enough air in your tires.

The issues

Many people can hop one obstacle, but two in quick succession, less than a bike length apart, is not in my skill set.

With both train and tram tracks, there are two issues to assessed for every crossing and one item concerning your bike


How rough is the crossing? Is the road surface level with the tracks, or is it broken?
How wide is the gap?
How wide are your tires?


Crossing

Sometimes the road surface is not level with the top of the tracks, or is broken. If this is the case, cross as close to 90° as you can, as slowly as you can.

Tram tracks in good condition have a gap of about 5cm (2 inches). At worst they can be 10cm (4 inches).

Train tracks occasionally have a gap as small as 5 cm (2 inches) but usually have gap of about 7 or 8 cm (3 inches), and sometimes much wider.

For a level surface, the angle is dictated by your tire width and the gap. For typical 23mm road bike tires, the minimum angle I recommend for tram tracks in good condition is 30°, and for train tracks in good condition it's 45°.

Having said that, I typically cross tram tracks at angles as low as 20°, using what Daniel called levitation. 

As with many uncertain cycling situations, ride "hands and heels", with your bum off the seat, so that the bike can pivot under you. 

If you are crossing at a low angle, extend your arms and legs before you get to the tracks, so that your body is at it's highest above the bike. As the front wheel gets to the first track, pull the handlebars up, so that the wheel has little or no weight on it as it crosses the track. If you are clipped in, or are proficient at bunny hops, do the same for the back wheel. And repeat for the second track. Again: this is only good for narrow approach angles.

Another technique to use in combination is to steer so that your front wheel crosses at a greater angle than your overall direction of travel. The front wheel would follow a sort of straitish S bend.