Does Identity-Based Encryption actually solve any problem? Identity-based encryption schemes[*] seem to have great potential in high-latency, delay-tolerant and mobile, ad-hoc networks since they apparently seem to avoid the need for key negotiation and exchanges. Used solely for key exchange, they allow any pair of members in the same group (however you choose to define it) to establish a unique pairwise secret that can be computed by each member up-front and as a function of their respective identities.
However, since each pairing based scheme - that I'm aware of - is predicated on a pre-distribution of some shared secret (e.g., the hashed ID of the agent raised to some secret integer), do any of these schemes offer any significant advantages over, let's say, a simple authenticated Diffie-Hellman (at least for purposes of symmetric key establishment)?
[*] Including pairing-based symmetric-key establishment schemes.
IBE is advantageous over standard asymmetric methods in one aspect, and that doesn't appear to apply in the case you're interested in.

In both cases, IBE and asymmetric methods require an enrollment process (whether to distribute secrets, or authentication data), so there's no real difference there.

However, when Alice wants to send a message to Bob, with standard asymmetric cryptography, Alice and Bob needs to exchange messages (whether to perform a DH exchange, or for Bob to send Alice his certificate).  In contrast, with IBE, Alice just encrypts the message with Bob's public id, and sends that message to Bob; Bob doesn't need to send a message to Alice.

So, that is the advantage of IBE; if you are sending unidirectional messages, you don't need a back channel to complete the exchange.  If this is important for you (for example, if you are sending encrypted emails; the store-and-forward email architecture doesn't allow a back channel), this is quite useful.  If you do have a convenient back channel (as in your case; you're going to exchange messages encrypted with a symmetric key anyways), it doesn't gain you anything.