On the fear about your two big clients — worth separating what you are actually afraid of, because it is usually not the rate.
In my experience the clients who leave over a reasonable increase are the ones who were already close to leaving, and price was the excuse rather than the reason. The ones who value the work absorb it without much comment, because the cost of replacing you is much higher than the increase. That asymmetry is the thing to hold on to: a new supplier costs them briefing time, mistakes, and risk. A ten or fifteen percent increase does not come close.
That is also why your position is stronger than it feels. Being busier than you want to be is not a coincidence alongside an unchanged rate for four years — it is the direct consequence, and it means you are currently the cheapest way for those clients to get this done. Cheap suppliers who are always busy are not in a weak negotiating position, they are in a strong one they have not noticed.
The honest risk is concentration, not price. Two clients being most of your income is the actual problem in your message, and it will be true at any rate. If one of them does leave, the increase did not cause that exposure, it revealed it.
Which argues for doing it now rather than later, while you are busy and have leverage, rather than after a quiet quarter when you feel you cannot afford to.