Negative or Positive Consequences If I Delete a Heavily Linked To Page On My Site?

Let me explain......

This site was hit by Penguin, and I am 99% sure that the biggest reason was that the link profile for the site has one page(well, a post actually) that has a LOT of sitewide backlinks pointing to it with EXACTLY the same anchor text. This was because I(foolishly, in hindsight ) bought some blogroll links on Fiverr last year and they are mostly sitewide ones.

When I run my site through the various backlink checkers, it comes back like this(different niche, just using this as an example) in the 'referring pages for anchor phrases':-

Dog Training Secrets Review - 1,904
How to train a dog - 220
No text - 90
Dog training advice - 74

....and so on.

I have actually reduced the amount of links to 'Dog Training Secrets Review' by asking the Fiverr sellers to remove my links. This is happening gradually though(anything up to 150 sitewide links per day). I have also generally been improving my site, not making it so 'SEO optimized', adding more content, not being too heavy with inter-linking and anchor text etc etc. Generally just making it a much better site for visitors. I am also slowly building more quality backlinks. It has always had a decent amount of quality backlinks, but those sitewide links have hurt things.

Before Penguin, I held the number 3 spot for a pretty big keyword that brought 100-150 visitors on autopilot every day. I'd be lying if I said I didn't fall into the trap of relying on Google That isn't the case now, but it's always nice to have a decent amount of organic traffic too. With the recent changes I have made, I am seeing improvements. My site and its pages are appearing for a few new keywords, but I'm still nowhere for the big 2 or 3 I want.

My plan was to keep making these changes, keep adding content, keep building quality links and then to approach Google and see if they would reconsider my ranking. But now I'm wondering if I could speed things up by simply removing that page/post('Dog Training Secrets Review'). I can easily take some of the content and merge it into another fairly similar article that I have on there.

What would be the consequences of doing this? I'm gradually losing links to it anyway. I feel like doing things this way might speed things up, but I want to be sure first.

Any help and advice much appreciated