To my mind you already have "sponsored" articles, they are just for one of your owner/contributors
e.g. http://www.in2town.co.uk/news/gastric-hypno-band/the-secret-to-weight-loss-is-inside-you-says-gastric-hypno-band-expert#.UEd-5cHN9X8
Adding other sponsored links would only diversify the content, potentially get more quality content on the site and make it a better user experience.
To me you could manage the relationship with the readers and outside businesses your team are involve with in ways that visitors will gell with more. This covers the top banner (which looks like an external paid banner when someone is on the home page rather than something a regular contributor is involved with. There are loads of spammy looking gastric band promotions out there and you have real potential to both improve this site and generate more trust with potential gastric band purchasers by showing the relationship differently so they see the person behind the product and banner. Also I see it is a Liverpool number that is given, I do not know whether Gastric band some of the other services that those involved in the site provide are local and the extent that they are fine to be purchased by people across the UK and beyond - If services are localised around Liverpool then having the ads in such a dominant place may not be optimising your ad revenue (which could always be put on Adwords Display Network and optimised around Liverpool if that is the case. I tried to click on the banner too for more information and it did not lead to more information. I wanted to know enough in answering this question to click on in and not being able to annoyed me (only a tiny bit) but would add to user experience and improve conversions.
Also whether you think you do or not, you do sponsored posting and there is absolutely nothing wrong with that from a user experience perspective as long as you convey it in a way that meets both the needs of advertisers AND viewers.
I think you have been given the right advice in terms of optimising conversion from an individual visit but the wrong advice more generally. As well as a new visitors clicks you also want to engage with them so they dont hit the back button, facilitate social sharing and provide a quality user experience so that they are going to engage more with the site then you want to have less banners in different places than you do currently. You want to make it easy for people to share the articles with others and enable your readership to grow which can make all your advertising perform better.
Others have mentioned that there was some slightly dated content that was still high profile, this is obviously bad for the type of site you are doing. You also mentioned in a positive sounding way that it was all your own group of people that were writing content which is actually a bad thing and the two points are connected. Would I keep coming back to reading posts at SEOmoz (before I became pro and come to use the tools) if it was just Rand and other staff posting? Perhaps but no where near as often. I have welcomed the whiteboard fridays with different perspectives and different expertise, I like the fact that I get access to hundreds of experts here with different perspectives and this would not happen without guest contributions. Also it means you can have much more content without having to write it all. Ok you might give a link away but as long as you ensure that the articles are of high quality and only a minor proportion are clearly sponsored (and do not make this too deceptive) then all you are doing is making your site better with more varied content and sponsored posts are less damaging to user experiences than big banners.
I will stress that I am completely not the demographic for your site. If I had my way google would give out moderate penalties for articles less than 1500 words and bigger penalties for articles less than 1000 words and gossipy type topics would also get google penalties unless searched for explicitly so "news" would not give xfactor or celeb stories in the SERP results.
Also the most relevant people for you to get views from is your users and it does not look like you have all that many links to your site at present which will be harming your SEO. You may want to look at getting some sponsored articles and enhancing SEO as well as addressing some of the user experience issues.
But it is a pretty good site considering it is no-ones main concern.