drawing too much current out of regulator causing heat, alternative 5v regulation methods?
There are two entirely different questions here.

First, is it possible to drive more servos using 7805s? And how to keep the regulators from getting hot?

Yup. Use one 7805 per servo, and buy some heat sinks. I've seen 5 volt, 75 amp power supplies which used linear regulators. With really hefty heat sinks and forced air cooling.

Second, what other ways are there to produce 5 volts?

In a word, switching. Since this site does not allow specific product recommendations, Google "5 volt switching regulator". Of course, you'll need to know more about what you're doing, since you'll need to ensure that switching noise does not cause problems, but you'll get much higher efficiencies.