HiFiman make a unit specifically for connecting things like the HE6 to a speaker amp The HE Adapter http://hifiman.com/Products/?pid=104
If you go down the speaker amp route you need to factor in that the sound flavour of the amplifier will have quite an impact on the balance of sound from your headphones.
This is much the same as using the speaker amp bias energisers with electrostatics Stax/Jecklin
You might like to consider a tube based amplifier where you can roll the tubes and change to overall flavour of the sound. You should only need something low power say 15 watts or so so may work out cheaper than a dedicated headphone amp. Some headphone amps have speaker outputs these days so might suit both purposes. I would suspect a SS speaker amp might be too bright for the HE6 but i'm not that familiar with it. There is the NVA personal amp which drives headphones and speakers. http://www.ebay.co.uk/itm/NVA-AP10P-Personal-Integrated-amplifier-/270505082352?pt=UK_AudioTVElectronics_HomeAudioHiFi_Amplifiers&hash=item3efb5bfdf0
There are lots of good 70's/80's japanese integrated amps you should be able to pick-up for under Euro 50 to give a speaker amp a try (i.e. Pioneer, Sansui, Trio, Rotel, Technics, JVC etc)
Look, I'm not into picking a useless fight over this topic, especially not while sitting jet lagged behind my desk at 5 am on a weekend. But I'm totally not convinced that the contention that you need a speaker amp to get the best out of the 6 is true. I've auditioned it on a couple of those so far and none of them convinced me. Let's just say that the entire headamp pushing scenario on threads like the HE-6 thread lacks nuance, to put it mildly. I'm sure you'll agree that they also present risks and disadvantages, especially if you also own other headphones. And just like the HE-6 certainly won't work on many headphone amps I'm convinced it'll also have problems with many speaker amps, for various reasons. This is a point that's often not mentioned.
But ok, I don't actually own a speaker amp and want to get to the bottom of this and that requires more than just a quick audition. You run it on the FirstWatt F1J, correct? That's not an easy brand to source in the EU (won't even mention India) and for an experiment the sticker price is a bit rich. But I'm willing to put my cash on the table to test my assumptions so if you have a recommendation for a speaker amp that DOES in your opinion get the best out of the 6 then I'll purchase one next time I'm in Europe, snap some pics if anyone requires proof and do the comparison. I'll drive it via my V800 DAC and compare with the V200 amp and the 337 dual mono tube amp I own and let the chips fall. Preferably something easily available in Europe, price upto 2K USD (lower is evidently better) and no-frills, no flickering lights, no sales BS and no gadgets. Looks are not a criterion. I'll use it wirth the 6 but if it also drives the 500 and my Senns that's a bonus.
If I like it better than what I have it'll stay, else I'll sell it on, done more stupid things in my life than wasting a couple 100.
BTW: nice review you wrote.