I am not qualified to advise you what diameter for 3.05m battens. I will just make some remarks in case someone else who has rigged a similar size boat will chime in.

Your wood battens (3cm x 2cm) do seem rather light. On a sail with roughly the same length battens, I made mine from two layers of 2.8 cm x 1.8 cm pine timber, screwed together with the sail sandwiched between. That's a total of 2.8 cm x 3.6 cm. I am not sure if this is too heavy, but I think not - they seem to stay stiff in the horizontal plane and I have not had one break from sailing forces - but if I haul too hard on the downhauls they do bend slightly in the vertical plane. I am satisfied with that dimension for myself. (Actually I copied the dimension and the method from James G (boat River Rat) a similar size sail, or slightly bigger, and as far as I know that has also proved satisfactory for James. It's probably not the best way, but it does the job).

The problem I foresee for you is that evidently you have made batten pockets to fit the perimeter of your 3x2 battens - (10 cm) - I see that approximately matches the circumference of the 25mm aluminium tube you are considering (at a loose fit), and I am guessing that is why you are looking at that size. I think you are probably going to receive the advice that 25mm is too small a diameter for aluminium tube (I may be wrong) and, of course, if you use bamboo this could be too small as also I guess you really do need a rather loose fit to get bamboo battens to slide in. Maybe you could stretch the pockets up to 3cm diameter for a tight fit aluminium tube, though I don't know if that is enough anyway. 

[By the way, another member (Johan U) has posted a useful article on facebook regarding his recently-fitted bamboo battens - and if you see this Johan, maybe you could post it here for other members.]

I think if you want to use aluminium or bamboo, I am guessing you might be faced with having to sew bigger batten pockets onto your sail - perhaps someone else can chime in and confirm or deny this.

An alternative to sewing new batten pockets would be to put a row of eyelets along the batten pockets and lace each batten onto the sail using a single length of cord, in the way Paul Th invented for Zane's sail (boat Pango). That way you could easily attach bamboo battens, and probably attach aluminium tube battens of the right diameter in the same way. I seem to recall Paul saying that putting in the eyelets (which he did in his usual conscientious and high quality way, with suitable reinforcement) was more trouble than making batten pockets would have been. However, since you already have extra layers there, perhaps it will be sufficient to just punch ordinary brass eyelets through the sail and the batten pockets, in which case it might be quicker than making new batten pockets. I don't know if this is a good idea, I merely raise it as a possibility. Maybe Paull will comment.

If it were me I would be looking to save time and money, and probably stick with two part wooden battens, a little heavier this time, and the two halves screwed together with the sail and the batten pocket sandwiched between, as I have done. Using that marvellous invention, the battery-powered drill/driver, the strips of wood can be can be put on or taken off in a jiffy. Wood is quite soft against the mast, which is a good thing. I think you would be safe with the dimension James and I have used. But I must admit it is a "quick and dirty" solution which means putting screw holes through your sail, and the resulting sail bundle will be possibly a little heavier, and some people would perhaps find the result looks a little "agricultural".

I note that your other spars are carbon fibre (lucky you). In that case, could you afford the sort of battens Davit T (ex Weaverbird) has written about ("poltruded? I am not sure if they are carbon or GRP) -  and if so, would 25mm diameter be OK? Perhaps David will know.