Bridge hand with high card points between 1NT (15-17) and 2NT (20-21)
I think it is tricky to stuff your artificial 1D response into the rest of SAYC.  When you consider the standard bidding structure over 1NT and 2NT, the pattern is that the weaker hand shows its shape as quickly as possible (via Stayman or transfers, for instance) and then either signs off, bids game, or invites to slam (giving the strong hand control in the latter two cases).  It is difficult to replicate this pattern after 1C - 1D because the opener would need to make another forcing bid in order to give the responder a chance to show his/her shape.  The best I can think of is to treat 1C - 1D - 1NT as an artificial force with systems on, but the usual systems over 1NT often terminate in 2NT or part-scores at the 3 level, both of which are too high if opener has a normal 1C hand and the responder is weak.

So I think you more or less have to pick one of the following two frameworks:


SAYC: The first two calls are normal, and a jump shift by opener (with cuebidding in competition) shows 18-19 points.  Responder can't pass with 7HCP, so you don't miss game, and s/he has some space to show features (like 4 card majors).  SAYC full provides two additional tools for handling some tricky edge cases.  The first is structured reverses for showing 5m/4M shapes; for instance, 1C - 1S - 2H is a game force with 5+C and 4+H.  The second is 4th suit forcing for finding difficult fits without wasting bidding space; for instance after 1C - 1H - 1S - 1NT, declarer can bid 2D to artificially force to game, giving responder the chance to show 5 hearts or other features.
Strong club: If you want to really pursue the reasoning behind your 1C agreement, you can choose one of several strong club systems (such as the precision club).  In these systems 1C is artificial and shows any hand with 16+ HCP, the thinking being that these are the hands where you want to have the most bidding space available.  This has all of the advantages of your approach, but since 1C can't be just 13 points you can use your usual systems without worrying about ending up too high.  It also allows you to use bids like 1NT and 2NT preemptively, which can make life quite hard for your opponents.  The downside of these sorts of systems is that they can get quite complicated and awkward in certain cases.