Sure, you can use an audio amp... but...
Audio amps are designed to drive loudspeakers, so you'll have to make sure your load is "similar enough" to a loudspeaker. That includes DC resistance (DCR): most 8 ohms loudspeakers have 6 ohms DC resistance and 4 ohms speakers have about 3 ohms DCR. So your coil should have at least 3 or 6 ohms DCR to suit an amp specified for 4 or 8 ohms speakers.
Next is inductance. Lots of audio amps play fast and loose with the safe operating area of their output transistors. If you use high power at a frequency where load inductance causes current to be significantly out of phase with voltage, the output transistors will really test their SOA. And most audio amps don't have real SOA protection because it's quite complicated to do it right.
The Mitsubishi amp is a very expensive collector's item, if you have one please don't blow it in an experiment. The Crown amp is also pretty expensive on ebay. Its service manual enter link description here has a SOA graph on page 7 and you should check it.
So I'd recommend a class D PA amp which will be efficient, cheap, and avoid SOA issues.
You can also use a cheap Chinese class D amplifier or module, probably something based on IRS2092 if you want 300W. All you have to do is increase the value of the input coupling capacitor, you can solder an electrolytic cap in parallel with the existing cap. If you want to go down to DC, then an amp based on IRS2092 will do it if you remove the input coupling cap.
Class D amps based on other chips would probably work too, but if it's a single supply bridged amp it might be a bit more complicated since you'll probably have a single ended to differential conversion followed by 2 coupling caps to the amp's differential inputs which are usually biased at some positive DC voltage.
So I'm recommending an IRS2092 based amp, or other similar chips which use positive and negative supplies and zero volt referenced input voltage, that keeps things simple, no DC offset to handle.
Note if you use a H-bridge driver instead of a class D amp there won't be any feedback, so power supply ripple voltage will get into the output. May not be what you want.
I don't worry about drift since my system is feedback controlled by measuring the magnetic field.
Well, that feedback loop may be a problem since the amp will introduce a bit of phase shift, be careful about that...
IRS2092 datasheet shows typical schematic, with the input AC coupling cap that should be shorted if you want DC...
Check the eval IRAUDAMP7 eval board schematics page 20 -- there is no coupling cap which means the chip supports it and this goes down to DC...