A standard extension of ECIES for multiple recipients (broadcast / multiparty)?
When I do ECIES, can I omit the MAC $d$? An attacker doesn't gain
  anything by tampering with the session key, since that just causes the
  inner decryption or MAC check to fail.


I wouldn't rely on that property. Please don't do this.


  Can I use the same ephemeral EC pair $R=rG$ for all recipients?


Yes, you can do this. NaCl in principle does the same thing, but uses your own (static) private key for the key-agreement, while you make the $r$ temporarily your private key (for this message).


  Can I use the same IV for all invocations of the symmetric cipher
  (once per recipient in ECIES, plus once for the message itself)?


Yes you can do this, guaranteed that you always have distinct keys. The DH-style key agreements will guarentee the different symmetric keys for each recipient. The encapsulated symmetric message key will also be distinct so it's safe to re-use IVs here. An alternative suggestion would be to re-use the IV, but add some small value (like 0 for the actual message, 1 for the first recipient in the list, etc.) Generally you shouldn't re-use IVs if you're not sure whether all keys are unique.


  If the total length of my session keys is the same as the length of my
  $KDF()$ output, then can I get rid of the symmetric cipher $E(k_E;m)$ used
  within ECIES entirely, and replace it with $k_E\oplus m$?


I'm surprised you don't already do this. You can let your KDF generate a stream of key bytes (KDFs can output arbitrary length keys) and use them as stream cipher. This is an acknowledged variant of ECIES and is actually standardized and implemented for example in Crypto++ and BouncyCastle.