The batten has the charm that it is unbeatable cheap. 40x60 even at premium-price-Obi 1.69 EUR/m.
It is also the question at what distance your collar beams are, right? For me, it's 890mm, and even 23mm thick wood bends very noticeably under my delicate own weight.
Going up to 28mm or higher quickly makes the whole thing ridiculously expensive...
I will therefore, as you initially planned, nail battens to the collar beams and then nail battens crosswise to the collar beams at 40-50cm distance. You can then lay them staggered at the joints, so you don’t have the problem of the small bearing surface. On top of that will come 23mm shuttering boards, which are also nicely cheap to get.
To really feel comfortable with an 890mm bearing distance, I would probably need something like 35mm boards... okay for a terrace, but not for a storage room for junk and odds and ends :p
