In the Hellcat (from another thread) I'm using the cheapo HK radio that you have mentioned having. Those receivers are spec'd at 6.5 volts max., and I was using a 2 cell lipo with a BEC. Decided to try the 2 cell, 700 mah LiFe battery which would be a nominal 6.6 volts while running. Long story short, I got rid of the BEC and just use the LiFe straight into the receiver. The servo is plenty fast and there is no heating or glitching to the receiver that I can tell. Of course, if your receiver is spec'd at much less, then you may (probably "will") want to keep using a BEC, so no point in changing to the LiFe's.
Out of curiosity, why did you get a 3.3 v. BEC? I guess if it works, then it works. But I have 4.8v and 6.0v stuff pretty much ingrained in my head after all these years and can't even conjure up a reason to design a 3.3 volt receiver unless its for some indoor RC that uses a single LiPo for a battery.