Is it safe to use shared secret as a symmetric key in one way communication?
Consider a device A and a device B. Let me paraphrase what I believed you just said. 

Communication happens only from A to B. We have public keys $PK_A$, $PK_B$, and the private keys $PrK_A$, $PrK_B$.

Devices A and B apply the Diffie-Hellman key exchange protocol to obtain a shared secret, $SS$. You say that it is logical to use $SS$ as a key for AES symmetric cryptography. It is sensible that the shared secret obtained from the DH protocol is used to derive symmetric keys from. 

You say that the shared secrets derived from DH are not uniformly distributed. This is indeed the case. Hashing the obtained shared secret will solve this, as any different shared secret will produce a vastly different digest. $K_{AB} = H(SS)$ 

Let $r$ denote a random number. You propose $H(SS|r)$ (appending pseudorandom numbers, then hashing it) but this is will not result in a differently distributed digest space than omitting the $r$. You'll have to communicate $r$ to $B$ as well so there is no security gain but only a costs increase. 

You also said that in the case of $K_{AB}$ being compromised, at least one of the devices must change its key pair. To my understanding this is not true. A new Diffie-Hellman key exchange can take place with different domain parameters, since the private keys of A and B are not compromised in this scenario.