Hello AeroEngr. I have the HF3s (which are HF5s with smartphone controls/mic) and I found the bass to be, well, "thin" (*gasp* audiophile blasphemy!) compared to some of the other headphones I own. The thing I noticed about portable amplifiers is that while they may do wonders in boosting the sound in general, they will not really help in tuning the sound to your preference unless the amp has a dedicated equalizer and/or bass boost. Have you tried to use an equalizer on your android phone? Those results may tell whether the HF5s will suit your needs or not, even without resulting to connecting to an amplifier.
I have a limited exposure to source components, but from the sources that I've used so far (which includes various iPhones, iPods, MacBook Pros, and the venerable Sony D777 CDP), I've found that using the equalizer helps bring out the bass I want more than the old CMOY Altoid Can amplifier that I have.
I took the plunge, however, and bought the FIiO E17 recently and I can say that boosting the bass level on that device definitely gave me the bass emphasis I wanted. I can honestly say that the E17 is a marked improvement over listening straight out of my source components or using the old CMOY amp (which didn't have a bass boost like the newer ones have).
I specifically mention the "bass boost" function because as you may already know, the FiiO E6 also has a bass boost function. I have never listened to the E6 but from my experience with the E17, the ability to directly control the bass definitely helped in the bass department while maintaining the clarity of the HFs.
The last thing I want to say, however, is that any portable amp is going to increase your bulk considerably and reduce the portability. I think you should try to tune your music using the onboard equalizers on your phone before trying out amplifiers which may or may not suit your needs. While I do enjoy the sound that comes out of my CMOY and E17, I find myself just plugging my HF3s into my iPhone or iPod straight and using the "Bass Booster" equalizer setting more often than I'd like to admit...