Under "standard" tournament rules, let's say you're playing a battery with 30 points worth of constructs... can you switch said constructs, from game to game? Let's say I declare a 10-pt countruct (say, catapult), can I switch it in my next game (before the game starts) with the crossbow, or even one of different cost?

In my venue they say this was the case for the black belt, and I'm wondering if it's the case here too...

The difference between the belt and battery are in the way you cost the items for your team. These are straight from the card.

Utility Belt
Cost - Utility Belt costs 7 points, plus 1 point if the Costume slot is active, plus 1 point for each Utility Belt Item slot that will be active this game (other slots are inactive). At least one Utility Belt Item slot must be active.

Power Battery
Force Construction - The Power Battery must be assigned a Power Ring (ring symbol) and 1-6 distinct Constructs (construct symbol). The Power Battery costs 2 points, plus the combined cost of the assigned Power Ring and Constructs, and must total a minimum of 16 points. The Power Ring and Constructs are all attached to the Power Battery at the beginning of the game.

So in the case of the belt vs battery, you are paying for the slots on the belt but you are paying for the distinct constructs on the battery. Therefore, once you pick your constructs for the tourny, those are the ones you need to use.

Also in the case of the belt,
you do not pay for the items, and you do not attache them till after the forces are reveled, and there for can change from round to round.

but for the Battery,
the constructs are attache during force construction, not during setup. so they can not change from round to round.