Hi,
a raw, not absolute explanation:
You can get cheap envy24 sound devices at Ebay, they provide +4dB and
-10dB for the IOs. +4dB is used for professional audio and -10dB is
consumer level. The phones output of your Laptop should work too, I
suspect the audio engineers didn't like you or they had no knowledge how
to fix the issue. Anyway, the sound quality of an Envy24 audio device
will be much better than that of you Laptop's onboard device, epecially
better than the output of the headphones amp. There are professional
audio devices available, that do sound much, much, much better, but they
are beyond your price limit. You could try to get an Art Tube Pre Amp,
at Ebay too, this is prosumer, but also used by professionals. They are
cheap and good.
Regards,
Ralf