Hey there! I've put in a low bid to get your attention as i'm still starting out on this site, and i'm happy to do the project for the listed amount if you'll agree to write me a good reference if i do a good job (which i will ;)). I've just finished a master's degree in mathematics at the University of Melbourne and i think i know exactly how to help with your project, seeing as my specialization is in probability in particular modelling interest rates and there is a lot of dealing with volatility curves in that area of financial mathematics. In fact i've done exactly what you're looking for except it was for calibrating parameters for the G2++ interest rate model by using a martingale approximation method to obtain the implied volatility curves from inverting swaptions (which made it a particularly complicated project) and it was done in R as it was one of the building blocks for my masters thesis (for which i obtained a distinction). in your case you're looking at stocks (or so it seems) rather than derivatives, which usually 'm also familiar with the methodology for using inverted caplet data to produce implied vols in the black formula. I'm happy to have you contact me so i can tell you exactly how i would proceed with your project.
p.s i have just gone through the slides you attached again and it seems like everything you need is already on there in Dupire's formula except for the treatment of the derivative, but from what i know this method is a outdated and most calibration is done using the Brigo and mercurio Dynamic volatility model or variations of it, which is more complicated but more stable in that you avoid the need for numerical integration but as mentioned it's pretty advanced stuff. if you are looking for someone to code Dupire's formula then i definitely do it in 5 days tops :-)
cheers,
Niresh