That (the ACD thing) is a die hard myth!!
Numerous experts (below is one example) have written on the topic yet people continue to believe, quote and thereby spread the myth! Sorry, I am not venting to you, just can't help but feel you are one of the many "victims" of those responsible for spreading hearsay, misconception and myths.
I may not agree 100% to the following, suggested by a Yamaha product manager, but I do think he is largely correct, much more so than those who continue to emphasize the importance of the ACD ratings on the internet.
The All Channels Driven Amplifier Test Controversy | Audioholics
The 180/250 W 8/4 ohm Hypex amps will only make a difference if you actually need the extra "watts. That's why to answer your question you need to use that SPL calculator. You have done that already so now you know 125 W average will get you peak spl of 102.5 dB, that's only 2.5 dB below reference level.
Now, ask yourself how often do you listen to 102.5 dB SPL? Also keep in mind 125 W average means 250 W peak so if you watch a THX movie, the 4700 can actually deliver 105.5 dB and that's full reference level!!
On the practical side, for the split seconds to even a couple seconds of such peaks the AVR likely can handle two or even three channels peaking to the same level, especially when you set the crossovers to 80 Hz or higher.
So in your case, I highly doubt you would hear a difference because a) those amps, Monolith, Buckeye, or VTV don't/won't give you double the output of the 4700 and b) doubling the output = 3 dB more spl, not more..
If the loudest spl you can tolerate for more than a minute or so it 10 dB below reference, then your AVR will only have to hit 95 dB peak SPL or 92 dB SPL average, and it would then have to output 12.5 W average. The AVR should be able to do that all day with 7 channel driven simultaneously, if well ventilated especially with help form an ext. fan.
The external amps will help taking some load off the AVR so it may run a little cooler, but you can achieve the same or more simply by using some quiet USB powered fans.
If you do add the amps regardless, you initially will likely hear a difference. That happens to many people including me, and it is a good thing because if you spent the money you should hear a difference (better of course) and you deserve the added happiness. Reality is, you really hear the difference because.......
Would I still go for the amp, of course, but that's me, I really like amps, preamps, dacs et......