I think you might be thinking about it the wrong way.
If you’re mixing and want to ‘calibrate’ for broadcast then measure using broadcast loudness measurements instead of RMS.
So if I were you I would lower the level of that file to -24**LKFS** (use Control Room metering to measure this) and then just adjust monitoring playback level to where you want it. You should then be able to play back a final mix of something that conforms to -24LKFS broadcast and it should feel appropriate in your room. It won’t matter if you read an SPL of 76dB, 79dB or 83dB. It’s of no consequence, because your room dimensions and more will determine what is comfortable.
Does that makes sense?
The way I see it is this:
You either have to conform to a monitoring standard or not. For cinema we typically have to in order to know what we’re doing. In other words, if we want to use a Dolby format we need both Dolby calibration and Dolby certification. Even without expensive certification calibration according to Dolby specs would be beneficial for cinema.
Now, if you’re doing broadcast then we actually don’t have a set standard for monitoring. This means that “79dB for mixing for broadcast” is basically an arbitrary number on your part, and so is -20dBFS Dolby pink noise. Those numbers might be close to where you end up, but they aren’t set in stone and aren’t an actual standard.
The way I approach this is purely practical. I want to calibrate my monitoring environment for two main reasons:
1: So that all speakers output the same level. If they don’t my panning would get messed up.
2: So that I can “mix by ear” and get very close to the broadcast loudness specifications I have to comply with.
So with that in mind the way I have done it is basically just grabbing a signal and then measured SPL from each speaker to satisfy my requirement #1. But for #2 - which is what you’re attempting - I actually prefer to simply play back a test file at -24**LKFS**, and I then simply adjust the output until I think it sounds loud enough, a level I would mix at. Once I have done this it means that I can mix by ear to that comfortably loud mix level I like, and it will be very close to -24LKFS.
It’s also worth noting that you have both a “reference level” setting and a dim setting in Control Room and they’re very, very handy. There are weeks where I have so much work that in order to keep my ears from getting tired I actually mix at a lower level than reference. With Control Room it’s very easy to mix at that lower level and with a key-press on my keyboard I’m back to reference, so a quick double-check of levels at reference is super easy.
In other words I can mix comfortably at my home studio and end up close to spec, every single time. I’m typically actually within spec normally, i.e. I hit -24LFKS +/-2dB (for US broadcast). And I have no idea what my SPL is in my room (because I can’t remember and don’t care).