Unless I'm missing something, the John/Nick situation is NOT a unilateral Carlill situation. There are obligations going both ways: John to find the dog and Nick to pay the money. A Carlill-style contract is unilateral because the obligation only goes one way (the person using the smoke-ball did not have an obligation to do anything, only Carlill had an obligation to pay-out if someone accepted the offer).
Think about how the obligation is construed in this second contract. Is the obligation to find the dog in favour of Julia (in which case Nick is contracting for the benefit of a third party and the obligation to find the job doesn't actually change making this a Williams v Roffey situation) or is it in favour of Nick?
It is also at least conceivable that the £200 is supposed to be backing-up the £150 rather than an additional obligation - i.e. a guarantee (with an extra £50 bolted on, admittedly) - which would mean that the maximum John could claim is £200 and not £350.
These aren't massive issues but do think very very carefully about how particular words and courses of events might be construed - don't jump to conclusions if you can possibly help it.