I would go so far as to claim that it is impossible to win this fight with a Solo Sorc without using multiple planetars (if you think you can do it, please tell me how).
Demons... control a demon army. You dont really need an army of planetars... one or two will do at the right time after Mel shows up... but I never needed more than one Planetar.
What you suggested is heavy cheese... but thats okay. What I suggest is actually more fun, but outright cheating (or pure cheese if you go the legit way by actually controlling the first bunch). I know that Mel will take alot of them away from you... but you can minimize that by keeping them coming. Go to the second pool and Ctrl+Q the 2 Nabassu there, use up all their Gate spells(3 each), then kill the original two as they are useless now. Grab your power to control demons. Each of the new demons summoned in are totally loyal to you. With luck, you got at least one more Nabassu... use its Gate spells. Your army is building...keep them safe. dont use them at the pools.
Move to the first pool and try to control the Nabassu there... if you get it, move it quickly off the pad out of danger. Try for the Balor next... although I usually fail, but sometimes get it too. move it away while you kill the remaining demons. Use all their gates. You should have an army of demons around 15-20 by now. Any new Nabassu... use their gates, but dont kill the second gen hosts. If you got Marileths and Balors too... then great. Dont throw away the Cambion Archers.... they will help immensely with Abazigal and Sendai later... and Mel.
Last pool... same thing. but dont take the final power until you have exhausted all your gates. Move them all onto the platform at the top... if possible, then take your power. The cutscene will start and you will be moved to the bottom of the screen... but not the demons:D Once the fighting starts, they will slowly migrate down and attack Abazigal, Gromnir and Yaga from behind... so all you have to concentrate on is Illasera and Sendai.
With this method I can usually get rid of two or sometimes three of the Five at the same time... making things much easier when Mel shows up. She will appear when the first of the five falls at Insane... but if you have twenty to thirty demons pounding on Abazigal, Gromnir and Yaga Shura at the same time.... you might get lucky and they might all fall simultaneously.
When Mel shows up she will use her Control the Minions of the Abyss... and generally takes away 50-70% of my army... so what? You've already taken out Abazigal, Sendai, Gromnir and hopefully Illasera... Just Yaga and Mel to deal with. Then use whatever method works best for you.. fighting demons taken away from you is nothing compared to fighting Mel at this point... they are easy.. and you can even take them back from her. Also, look for any Nabassu she gates in to control... and use their three gate spells quickly.
Last time I tried it I had 20 Cambion Archers doing heavy damage the Mel from the sidelines while I removed her protections, while my Marileths, Nabassu and Balors were taking care of her summons. I was playing a Fighter/Mage though... but it should be possible with a sorcerer too. Maybe a combination of demons and planetars would make this fight exceedingly easy on Insane... I dont know.
Cuv