Undiscussed Canape?

I am always curious when I notice sequences that call for an undiscussed canape approach.  I mean, sure.  Discussion is better.  But, some auctions just scream canape.

Here's an example.  LHO opens 1D, partner doubles, and RHO bids 1S.  You have 1-4-3-5 pattern with values to compete (if pushed) to the three-level.

One theory is to bid the long suit first.  The auction you anticipate is either:

1D-X-1S-2C
2S-P-P-2NT or

1D-X-1S-2C
X-P-2S-2NT

In either event, you expect partner to take the 2NT call as showing 4H/5C.

The risk to that is this auction:

1D-X-1S-2C
P-P-P

Now, you might score up +110 instead of +140, if partner has four hearts, which would be bad (especially at MP).

The solution is probably canape.  Bid 2H the first time.  The anticipated auction is:

1D-X-1S-2H
P-P-P or

1D-X-1S-2H
2S-P-P-3C or

1D-X-1S-2H
X-P-2S-3C

In the first auction, you might end up in 2H on a 4-3 fit, which could be bad.  But, on the last two auctions, you end up in the right place, as long as partner takes this as canape.  Why canape?  With 4-4, you could bid 2NT instead of 3C.

So, if all of this makes sense, it seems like an undiscussed (or discussed) canape approach works just as well as the non-canape approach if the auction has two bids.  However, if the auction dies with this initial bid, 2H gets us to the right spot when partner has four hearts (probably), but 2H might get us to the wrong spot when partner only has three hearts.

Tough problem.  Any thoughts out there?