Thanks all for your responses! Meant to get back sooner, but it's been a manic couple of weeks.
13901 - I think you're right, on balance. I am tempted by the peer-to-peer model, as I've used it successfully elsewhere, but I'm going to keep looking.
JMN57 - Am UK based, so we don't really do full coverage for rental cars here - the most you tend to get is CDW Excess insurance (which I used to always get when I was travelling regularly pre-'rona). Believe me, I've trawled every 'autonoleggio' and 'noleggio furgoni' place in the Barese area! Several are saying come back in May - they'll have a better idea of their stock levels and demand by then. It's an option. LIke you, I've looked back at my last overseas car hire prices: FAO, 3 days, £38; NTE, 7 days, €137; NCE, 3 days, €69; AAR, 7 days, £117... Ah, those were the days.
SanDiego1K - Thanks for the heads up re queues. I'll make sure there is sufficient entertainment for a lively 5-year-old! This makes the prospect of renting off-airport more attractive. Do you have a TR for your trip? Otherwise, I might start a Puglia thread on here and ask you for advice! This is my first flight since 2019, and our first family trip abroad since 2018, so we want it to be special! Great idea on the AutoSlash tracker, I'll do that - and as
BobFF68 says, I'll keep an eye on the prices in general.
I do have a couple of much better (read, less than half the airport price) quotes for Bari station, which is fine - a taxi or the metro will work, and it's likely less of a queue, but I need to be sure of the conditions (long story). Hopefully I can get that to work!