Suspending the ceiling with existing base battens

Hello dear professionals,
I have a question about the topic of suspending a ceiling.
I removed the old wooden ceiling and underneath there were 24x48 battens screwed directly to the concrete ceiling with a spacing of 60cm.

The old wooden ceiling is to be replaced with drywall, so I wanted to reuse the current drill holes and, ideally, the battens as well, but screw a counter-batten/support batten with a spacing of 40cm onto the existing ones, to which my drywall sheets will be attached.

However, the question arises: if I have the counter-batten 38x58 on the existing 24x48, I only have about 2cm of play for the screw in the wood, so my drywall sheet would never hold.

My idea would be to remove the 24x48, use the larger ones as the base battens in/to the existing concrete holes, and then use the 24x48 as support battens on top, to which the drywall sheets will be attached.

Is there a mistake in my plan and should it rather be done completely differently?
I am open to any suggestions.

Thanks in advance

Screw a counter batten/support batten with a 40cm spacing onto the existing one, to which my drywall panels will be attached.

Why? Can't you work with the existing battens?

The existing one has a batten spacing of 60cm. In my research, I read that when suspending with drywall, the support battens should ideally have a spacing of 40cm, and 50cm would still be manageable. However, the existing one I have is at 60cm. At least that's what I read and to answer your question.

The existing one has a batten spacing of 60cm.

I would leave it to the 10cm (Knauf says max. 50cm). Apart from that:

However, the question arises for me, if I have the counter-batten 38x58 on the existing 24x48 screw, I only have about 2cm play for the screw in the wood, my drywall panel will never hold.

Why shouldn’t it hold? Hang yourself on the base battens and try it out. I’m more of a pragmatist who tests first rather than arguing to death before starting. After all, a complete wood paneling seems to have held as well.

That's why I started this topic, if someone says 60cm is not an issue and possibly has it themselves and everything holds, I would trust that.

The basic battens alone hold really firmly and definitely hold me. It was more about, if I go the route of counter battens and screw them into the existing screw, I can't go very deep, only about 2cm before I reach the concrete ceiling. Here I was wondering if a 2cm screw depth for the counter batten still provides the same load-bearing capacity as the batten attached to the ceiling. I really can't imagine that it is, but I am also an amateur.

Hanging with drywall, the supporting battens should ideally have a distance of 40cm, and 50cm would still be acceptable.

Does this apply to all panel thicknesses, 10, 12, and 15mm, single or double layered? It should also work with 60cm (but not with single 10mm panels).