There is a nice little 1912 single motor for sale on eBay currently at just $8k. All the other parts you would need to finish the bike are available as reproduction parts and in time you could find several original parts to add to the bikes credibility.
There is also a 1912 single cylinder complete bike listed on eBay. It has been for sale for a long time now but I guess the sellers reserve price has never been reached. It’s up to over $40k already, so the single motor, complete with carb and magneto looks like good value.