matching transformers to improve voltage swing into higher Z loads? which inexpensive amps can swing 250 ohm loads to high spl levels?

[karlsonklam]

I have S.M.S.L.'s TPA6120A2 based amp and consider it a neutral and excellent value but seems to be lacking on voltage swing into 250 ohm Koss 4aat cans.  Using a well - recorded drumkit,Tthis amp can't reach the eye-blink level peak on the snare which comes easy with lower impedance headphones.  One way to improve the impedance match would be to try say some ~$12 Edcor 600:150 ohm matching transformers - the 78 ohm dcr of the 600 ohm winding might make things mushy.
 
since I don't have an easy way to monitor the peak to peak voltages going to the cans, this is a subjective matter.  -  -My Zhaolu's built-in headamp burnt up trying to drive vintage 250 ohm headphones.
 
 
seems like the very low impedance and Z 250 and up present challenges to little solid state amps.