No, the market doesn't need to know your selections. If the price on a certain outcome is consistently incorrect, which you infer by the insistence your picks offer value, then you can expect the market to "correct" over a course of time (the old chestnut of market efficiency, or a form of).I am unfortunately old enough to remember the introduction of three points for a win. It was introduced in England in 1981, but the number of draws there remained constant. However, in other countries, notably Turkey's top division when it was introduced there in 1987, the number of goals did increase quite significantly, (see picture at top), and draws decreased as a result.
It's an almighty IF to suggest your picks will continue to return 37% or so. Historically speaking, it's almost certain they won't. I don't know your sample size, but that figure seems to be based on just part of last season in which case the sample size is, of course, insignificant.
A big factor in draw expectations is obviously the total goals expected. I don't know for sure, but I suspect your projections fail to take this into account. The lower the goals the more likely the draw - obviously.
A salient point you make is "Draws will continue to hit overall at the rate that they have hit over many years". Yes, pretty much true, unless a big factor in the game were to change (e.g. extra points for goals scored or no points for a draw (ain't going to happen but I remember in the 1980s when the equivalent of the Conference, the Gola League I think it was called, offered 3 points for an away win and 2 points for a home win which should have changed the dynamics of a game. As did the introduction of three points for a win - which saw a pronounced increase in home advantage and, probably (haven't checked) an increase in goals and hence decrease in draws. Anyway, the point I was going to make is that the draw should indeed continue to hit at the same (well, similar) rate. And that rate sure as hell ain't 37%, even in the type of match you are predicting the draw in.
It's almost unthinkable that you can consistently hit at a % equivalent to a price of 2.66 on an outcome generally priced in the 3.3 - 3.5 range you mention. Sorry, but the market is never going to be that wrong in the modern age, at least not consistently.
Now, I'm not saying the draw isn't ever value. I think it is. But rarely is it the enormous value you make out. There are certain match situations - not confined to dodgy Italian results - which contribute to a likely (relatively) higher probability of a draw. But, in the main, this would probably involved getting a price of 3.25 or so on a 3.00 shot. Nice value for sure.
An important point which you haven't addressed is how you price the draw when your system predicts a draw. You can't simply back an outcome blind without looking at the price and, to the best of my knowledge, your system has shown no price sensitivity whatsoever.
Hope that helps.
I also do not intend to suggest that the ratings will continue to predict draws at anywhere close to 37.84%, (although I hope they do), but that percentage has a long way to drop before the strategy becomes unprofitable. I mentioned before that some draws are 'strong' and others 'weaker', and this is the number for the 'strong' draws only.