I doubt that there is a way to change the offering salary based on how you approach the company. While there are still cases where an individual manager has the power to sway the hiring salary, my experience thus far has been that HR has a controlling capability in most cases that leads to a fairly uniform negotiation process. I've heard of stories where a hiring manager can name their own price on incoming people, and force it through the system... but I've never experienced it for myself.
You have the interesting situation where they know you and your work, and you know the company and it's hiring practices. It really could go either way. Options include:
They'll make an industry competitive offer, because they know you'll leave if you don't have a good standard of pay (after all, you already have). They know what you can do, so you're a better bet than a guy off the street that they've never met. You'll be starting the job with a much lower learning curve, which is a big win.
They'll hold back - either because they are cheap, or because they don't want to start a precedent with existing employees. The model of "quit, work somplace else, come back 8 months later and get a radical pay raise" is not a good model for ongoing company stability.
The smart thing for them to do would be to make sure that existing employee salaries are at least somewhat competitive. There's usually a delta that is acceptable, but at a certain point the deviation between current pay and local industry standard can get too big.
Alot of this is not within your control - if your company is smart, the decision will be a matter of company practice that transcends an individual. If the hierarchy of decision making is fairly standard, it'll be something like this:
- Interview process to determine current skills and team fit
- Hire/do not hire decision from a manager
- offer process begins with HR
- in some companies, HR will go back to the manager or the person in charge of the money (may be bigger than the hiring manager) and vet the increases.
- in other cases, the company has a pool of money, and salaries managed very centrally, so the hiring manager/department head may be able to advocate for a high salary.
- this seems like a nuance but it can be a big deal - the coupling of budget and product means the options for much more granular (and creative) decision making.
What I'd Do
If you think of your former manager as a good advocate and someone you'd trust - reach out. Mention your interest in returning and ask what method of applying would be most appropriate. Don't be turned off by being told to use the formal application process.
After you've applied, mention to any former collegues and friends that you've done so.
Then leave it - hopefully you'll have generated some advocates and the company will be talking about it internally. The interview process may be abbreviated, since they already know you, or they may put you through the regular process for formality's sake.
When it comes to salary, stick to what you feel is fair. If you have justified a higher salary outside, and you want to stick to it - stick to it. Mileage varies tremendously here. I don't know about you, but I know that I'd take a minor pay cut to move from a situation I hated to one that I know that I'll like. Only you will know what it's worth to you.