Alternatives to motorized variable capacitor?
You have a large number of options.

a) Your link to motorised cap is indeed way over the top. However, if you can buy, or rescue from a junked radio, a vane-type variable tuning capacitor, you can buy a geared stepper motor for a few $£euro from fleaBay, and couple them yourself.

b) Although you say you only need 10% variation in C, it is usually unwise to use a variable capacitor as the entire tuning C. Far better to used a fixed capacitor, and connect a variable capacitor with a relatively large capacitance swing to it with a small capacitor. This has a number of advantages.  

The stability and resolution of the resulting combination is far better than that of the variable capacitor alone.  

The RF voltage across the variable element is lower than that across the combination. This is not so important if the variable is a vane-type, but could be very significant if the variable is a varactor.

If the variable is a varactor with a low Q, the Q of the combination will tend to the Q of the fixed capacitor, which you could choose to be higher.

c) You can adjust the inductor, perhaps by moving a ferrite core in and out of a solenoid, perhaps by making the inductor from two solenoids in series, and rotating one to change their mutual inductance, so changing the total inductance.