The issue

You become extremely aware of how many times the word said is being used.

Here are a couple of guidelines about said:

• The word said is one of the most frequently used words in almost every fiction. Why? Because you need to distinguish speakers from each other, and every other verbal attribution sticks out if not used with the greatest care.
• Listeners expect to hear it, and they will ignore it. Don't be self-conscious about repeating the word said.
• Make it as flat-pitched, low-volumed and generally non-noticeable as possible. Don't try to vary how you say it to break up the monotony. You will only make it worse.
• Sometimes the attribution actually helps the rhythm of the dialogue.
• If you are narrating your own book and want to leave out some saids, do it. If change of pitch or other clues are indicating which character is speaking, the listener doesn't need the attribution.