"If the amp is not specifically spec'd into 2 Ohms, it 's not very likely that it's capable at that load." That's not true 100% of the time (and I realize you indicated 'not very likely'). For example, the IcePower AS series (1200AS) indicates minimum inpedance of 2.7 ohms. That derives from the pro market where someone may be piggy backing three 8 ohm speakers. I had both an IcePower 1200AS stereo and dual mono amps and they drove (and sounded better too) my Thiel 3.7s than my Modwright KWA150SE in my system. There are two magazine reviews. One measured the minimum impedance at 2.4 ohms (at 125Hz) and the other at 2.3 ohms (at 120Hz) and both measurements indicated the impedance remains between 2 and 3 ohms throughout most of the audio band (the Stereophile plout shows something around 75Hz all the way up to around 20,000 below 4 ohms). I now have a modded LSA Voyager amp and it was no issues either. I also for a bit (since my system is an integrated A/V system) had a Class D Audio mini GaN amp driving the 3.7s for HT.
Peachtree Audio has a 4 ohm rating and indicates "The amplifier in the nova300 is capable of driving an extremely wide range of speakers with impedances as low as 2.5Ω and as high as 16Ω" So that should be fine with the 2.4s (as long as there is not something else crazy in the chain such as speaker wire causing an issue with that minium impedance - many moons ago I had an issue with a particular brand of speaker wire driving Mirage SM-3s which were not a hard load). The Yamaha noted by the OP, like many receivers, has an impedance switch for lower impedance speakers. I converted my front bedroom system to strictly a UHD HT (vs. an integrated A/V system) and the Onkyo receiver has a setting for lower impedance speakers (the only thing rated less than 8 ohms I use in the 9 channels is the Ohm Microwalsh Talls I have for front Atmos speakers and the room isn't big so I just left the settings as normal).
My 3.7s are in a large room that opens into other spaces and I can play it loud enough with no distortion and no issues. Sometimes, when my friend comes over during the week he asks me to lower the volume a drop.