If you cannot easily bend your elbows when on the hoods, or your hands, shoulders or neck gets sore then your stem is probably too long and possibly too low. A shorter stem redistributes your weight off shoulders and arm and toward saddle as well as making you slightly more upright - although the ability to bend your arms more compensates a bit. Stem length should be considered before height, but if you can get a stem that is a bit longer to allow more vertical adjustment that may help as well.

You should make sure saddle height, tilt and fore-aft are proper first, as all can affect distance to the bars and weight distribution. If there are resources near you for proper fitting of your bicycle that would be helpful. Often if a shop is not available a local bike club has someone who is good at it. You need to be clear about your style of riding so that you are not set up too aggressively.

If you are on your own try Google (bicycle + fit, stem length, or saddle position). Be prepared to be overwhelmed – it’s not as simple as some say. Bars should hide the hub axle, knee over pedal axle, and leg straight with heel on pedal are all common guidelines for stem length, fore-aft and seat height, and each has it’s weaknesses. One fairly solid guideline though is to not tilt the saddle forward.

I would not worry about twitchier handling. The stem and bar form two legs of a triangle on each side. The hypotenuse (imaginary line between outer edge of bar and stem bolt) determines responsiveness (degrees of wheel rotation obtained by moving the outside of the handlebars a given distance). Reducing stem length only affects the short side of that triangle, changing the hypotenuse by a very small amount.