Hi Pid, and welcome.
If your bun is in the truck you must NOT pack stuff up around it, certanly not ON the cage, or he won’t have enough air.
I would say the best place for him is on your lap (yes, in the cage!).
I have a big bunny. 19x12x10 is OK as a transport carrier and for very short periods but Java will be in the ‘loaf’ position rather than spread out so it won’t be comfortable for him. If you really don’t have any choice about the conditions of your journey and it’s going to happen anyway, then make it as safe and as comfortable as possible.
If you have a close relationship then on your knees will be the best place for him imo. You won’t be comfortable, but nor will he. Not on the floor if you can help it as there will be wind draughts and possible fumes collecting there.
The most danger your bun can come across is not eating, so you MUST ensure he eats or nibbles regularly and in my experience, this is when the vehicle stops moving. So take his absolultely favourite treat and make sure his digestive system has something in it all the time. And when you do stop (you’re surely going to have toilet breaks!! lol) make sure you entice him to nibble something, anything. And when you get to destination keep a close close eye on him and make sure he is eating and pooping as he should be.
You don’t say how long your journy is. Have a safe journey and let us know how you got on. Please.