I've built several servo powered walking robots. Torque is a major concern, and obviously weight plays a part in how much torque is required. The recommended servos look to be $30 each, x12 means $360. If you spent $200 just on servos you'd have to settle for $16 servos. Probably less torque. That would mean that at full leg extension the robot might not be able to support itself. That would be an annoyance when trying to focus on walking algorithm development, which is usually the fun part for these small walkers.

You can definitely do something for cheaper, but I wouldn't call this a joke. When I was 15 (20 years ago lol) I designed an 18 servo hexapod. I saved up $350 from cleaning horse stalls and my dad agreed to pay the other half, and I spent $700 on servos. It was great to learn about inverse kinematics before ever setting foot on a college campus!

Now we're curious about what part replacements you'd suggest.

Well don't be shy, post some videos of your $200 quadruped showing off its flexible dynamic gait performance.