If you can't manage within the generous hand baggage allowances, or fall foul of the size requirement, and you're stuck with an HBO fare you may wish to consider a POUG (Promotional Online Upgrade) to a cabin that automatically offers a baggage allowance.
This will obviously depend on whether the last leg is long haul or short haul as to the cost versus paying a lot of bag fees, and indeed you might find it's not offered at all. However, if it makes sense financially to pay, say, £79 per person for Club Europe you could wait until 48 hours before (by which time the offer would probably have popped up if it was going to) before deciding what to do about buying extra bags.
The other, more chancy, option is to wait until the airport if you don't get the offer beforehand and then enquire about an AUP (Airport Upgrade Price). If that isn't offered you'll be looking at a much bigger extra baggage bill though ...
If you can tell us the actual problem sector, we might be able to better guide you because we're guessing a bit at the moment.