I don't like laying em' down, if you have good chain w/ binders,or 2"wide ratchet straps AND good hard points at each corner, I say leave it up. arrange the chain, straps to pass through the throat (just below the dies) and to each corner. If you think you got more tie down chains than needed, think again, It's far better to use more than you think you need, especially if they're just cluttering up the back of the truck. Careful you don't tweak the trailer though. I wouldn't take it apart. Test the lift by picking the hammer up say 2" off the ground, if you can't, the truck is tipping.......forget that. If you can lift 2" get on the hammer and bounce, If that rocks the hammer/truck........forget that, If it's stable you're probly good to go.
The biggest hammer I've moved to date was a Beaudry #8, 200lb, upright. Big hammers are never laid flat, why do that with the smaller? Unless you have to.
That' my 2 cents worth.............mb