So, what about relationship dynamics in this setup? I think we must proceed with the two Shen Yuan fundamentals regarding relationships, which are:
SY will continue to blithely wifebeam everyone his peer group regardless of status, and
SY will have zero awareness either that he is doing so, or that any of said peers have anything more than a friendly platonic regard for him.
It takes a Luo Binghe level of blatancy and persistence to get past this guy's shields, and none of the Qing Generation have anything like that kind of shamelessness. So there's that. On Mu Qingyuan's part I think in this setup the wifebeam comes in because Mu Qingyuan has managed to replicate most of MQF's expertise, but has not managed the accompanying level of professional medical distance or coolness, so he's just Florence Nightengale'ing over everybody's sensibilities.
I couldn't decide at first whether it was better for Shen Qingqiu to fall in love with Mu Qingyuan or to (correctly) think he's trying to kill him, so I eventually decided on both in succession. SQQ actually twigs fairly early on to Mu Qingyuan's homicidal intent! He's quite sensitive to this type of vibes! But he doesn't tell anyone else because he can't prove anything (and he's not sure it's not his own paranoia.) And as time goes on and Mu Qingyuan continues to be nothing but friendly and helpful, Shen Qingqiu becomes less and less sure of his true intentions. I think in this setup SQQ sort of takes over Liu Qingge's role -- initially being the only one to suspect that something is not quite right with the newly transmigrated peak lord, only to over time fall under his sway and let his guard down.
If SQQ is falling in love with Mu Qingyuan, one might think that Yue Qingyuan would become jealous. Not so, if you're familiar with my particular headcanons about QiJiu they're coming into play again here. Yue Qingyuan is just so grateful for Shen Qingqiu to have another advocate, that someone other than himself is actually trying to help SQQ and that SQQ is letting them, that Mu Qingyuan immediately becomes his second favorite peak lord, and he will empower Mu Qingyuan for anything that doesn't involve blatantly crossing SQQ. So Mu Qingyuan gets all the budget and authorization he wants for extrajudicial night hunts searching for "cures."
Liu Qingge mostly gets dragged into Mu Qingyuan's orbit because he is the primary guy that Mu Qingyuan taps as bodyguard-slash-transport when he wants to go on missions to search out a rare beast or plant or enchanted item that Mu Qingyuan thinks will help him on his kill-SQQ scheme. (MQF in canon is more of a fetch-quest-giver, but Mu Qingyuan is a hands-on control freak kinda guy, so he goes himself.) Liu Qingge in this setup is I think kind of in Mobei-jun's role towards Shang Qinghua: he absolutely thinks they're courting and also thinks Mu Qingyuan is aware that they're courting and is just being coy about it. He is not.
Shang Qinghua has not noticed that anything has changed. Well, he has noticed a few discrepancies and gone 'huh' about them, but he's not doing anything about it.
All of this goes on for years and years (at least eight, maybe up to ten) in the liminal time period after the Qing generation moves up but before Luo Binghe arrives, until finally the disciple selection day arrives. Mu Qingyuan freaks out and panics because the canon is happening and he hasn't managed to kill Shen Qingqiu yet, and when SQQ demands Luo Binghe for his peak, Mu Qingyuan hastily inserts himself into the conversation.
MQY: Shen-shixiong, I highly recommend against taking this particular pupil onto your peak. His birth chart is uhhhh something something fire dragon and yours is IDK if you touch him your meridians will definitely explode.
SQQ: Stay out of this, nobody asked you, it's not like I care about your opinion! >:((
YQY: *also inserting himself into the conversation* Shen-shidi, if Mu-shidi has a concern about your health I think we should definitely listen to him. You can get other disciples!
SQQ, who didn't really want Luo Binghe in the first place: Oh very well. Take the brat and make yet another brute out of him, see if I care.
MQY: ....(Holy shit. Was that. Was that really all it took? All those years running around trying to game the system and that was all I had to do??)
And so Luo Binghe goes to Bai Zhan peak, but only for now, because you can bet your booties that Mu Qingyuan will not be able to keep his distance from THE BABY PROTAGONIST! OMG!!! for long, and will spend enough time hanging around BZ peak or whisking Luo Binghe off to Qian Cao to treat his training injuries that he is not going to stay off Luo Binghe's radar for long.
All of the Qing generation of peak lords can only watch in dismay as this budding ingenue seduces their PCP. Shen Qingqiu is confused but indignant that his favorite frenemy isn't trying to kill him any more. Yue Qingyuan will be happy to listen to him rant about it as long as he likes. :) Liu Qingge is outraged that he's getting sniped by his own disciple (but also kind of proud. The finest Bai Zhan tradition, winning by defeating your own shizun.) The end.