Honestly, I think the "inviting everyone back" reputation can and does persist in environments when a chapter IS NOT inviting everyone back. Look at the Indiana system where the "weakest" chapters are cutting lots and lots of women - and they still get that kind of reputation. You probably won't get very far trying to change the invitation system, and I would recommend putting your efforts elsewhere.
Your advisor is following the RFM (Release Figures Methodology) numbers that are given to all the chapters on your campus. There is pressure for every NPC organization to follow the RFM guidelines for each campus, because there can be penalties (less leeway, fewer quota additions, etc.) for NOT following the guidelines. There was an extensive discussion about it in this recent thread:
Dealing with mean PNMs
Here are other great threads on the topic:
The Best Strategy for a "Weak Recruiting" Chapter
Low-tier recruiting strategy
Do you know what DOES help with allowing you to release more women? Recruiting better. I have been the recruitment advisor with chapters that suddenly had significantly higher return rates than previous years', and thanks to RFM, there's a "flex list" that automatically releases extra women when you have a higher return rate. I've even gotten frantic early-morning calls to add more women to the flex list because we were able to release even more women.
Ok, end of RFM rant.
To your question about getting elected:
Do you research and your homework. Have a great plan as to what you'd do to improve recruitment. In my experience, most women don't really campaign for positions during sorority elections - but if you want the job - show the women that you have a plan and strategy.
Talk to the current recruitment chair and recruitment advisor. Let them know that you're interested in the job and that you'd like to learn more about what they think you should know about the job, what they're experience has been, what they would like you to do this year. It can really help get the buzz going for you if the previous recruitment chair is publicly backing you.
To be successful in your job:
I notice that most of your suggestions are PR-related. That is all probably going to be the job of the PR chair, so recognize that you're not going to be in charge of a lot of that. It can be a good cooperation with your PR chair, but it's a little tangential to your main job.
Your focus: CONVERSATION!!! I say this in almost every thread that pops up on this topic: the number one issue for most weak-recruiting chapters is CONVERSATION. To quote what I said in another thread:
In my personal experience, the #1 problem that weak-recruiting chapters have is that members aren't very good conversationalists. If you look through the recruitment stories on this site, it's an extremely common pattern: PNMs complain of awkward conversations at their least-favorite chapters. And it's a cycle: strong chapters tend to recruit the star conversationalists, weaker chapters tend to recruit the women who don't shine during formal recruitment and cocktail conversations.
Check out a couple of books:
I Heart Recruitment
How to Win Friends and Influence People
I bet that most people in your chapter don't have a very accurate picture of who your best recruitment conversationalists are. This happened in my chapter, too. We assumed that the most outgoing/well liked people in the chapter were the best at recruitment conversation, and this is not always the case. Look at having alumnae and/or advisors come in an do assessments (mock conversations) with each woman to figure out who's good, who needs work, and what people need help on.
Work on studying your PNMs ahead of time - KNOW them. Know how to pair them to your sisters based on shared interests in the first rounds, and then on personality in the later rounds.
If you're not pairing your PNMs to your sisters, figure out how to do that.
Did I mention work on conversation? Ya - do that. Also make sure that your sisters can talk easily about any aspect of your sorority and know what activities other sisters are involved in.
Read through the recruitment stories on here - you'll easily see what kinds of things are consistently influential to PNMs (hint: decor is rarely a factor, so keep it elegant and simple if you can).
Good luck!