The closest thing I know of to a complete statistical model of fantasy value is Football Outsiders'
KUBIAK projection system for redraft leagues. It's designed to predict next year's fantasy points only, and is based heavily on projections for the team's performance (they also have to use their judgment to assign the values for some variables, like players' roles). A complete dynasty model might need to be a mixture of one projection system like KUBIAK for short-term value (the next year or two) and another projection system for long-term value.
Another approach, instead of trying to make a complete statistical model from scratch, is to start with conventional wisdom (based on ADP in startup drafts, or other people's rankings, or trade values) and then to analyze data to find ways to improve on those consensus rankings. You could start with just a small number of other variables (in addition to a player's consensus ranking), like their position, years of experience, and where they were picked in the NFL draft, and see if you can predict career VBD better by including those variables than by just going with the consensus rankings. Every time you find a variable that helps predict career VBD (better than you could with consensus rankings alone), you've found an error in the consensus rankings that you can take advantage of - certain types of players are being undervalued or overvalued by other owners.
That way you wouldn't need to build a full model from scratch all at once - with the consensus rankings as your skeleton you could gradually add more variables and build a better and better model. Over time more and more of your model will be based on objective variables and it will depend less on the consensus rankings, and maybe eventually you'll eventually get to the point where your objective variables allow you to leave out the consensus rankings altogether, in which case you'll have found a complete statistical model. But even if you don't ever get there, the model can still do a great job of estimating value and of identifying undervalued and overvalued players, which is what you can actually use as a fantasy owner.
One possible downside of this approach is that you'd need the data from old fantasy drafts in order to be able to make it work, so you'd have to get that data and you could only go back as far as you have ADP data. Another potential problem is that the fantasy conventional wisdom may have changed over time, so you might just find flaws in fantasy owners' previous views (e.g. overvaluing RBs relative to WRs) which are no longer present in their current ratings. But the advantages could outweigh that - you'd be able to start out with rankings that already incorporate lots of hard-to-quantify information, so instead of having to build everything from scratch you'd just be looking for specific variables that let you improve on what other people are already doing. Plus, you'd have a great chance of doing better than other owners at valuing players, since the approach is to start with other owners' valuations and then find ways to make them more accurate.