With smaller Airstreams there are aluminum squares pop-riveted to the belly skin that mark four good locations to place STABILIZERS. Any lifting, even wrenching on a stabilizer, will deform the U-Channel frame underneath the belly skin and you risk stabbing through skin if it slides off.
As far as I know any true lifting must be done from the knifes edge of the vertical steel plate your axles bolt up to - and if I were cribbing up a 34' I'd use both ends of both plates to spread the weight (where it extends beyond the wheel & tire).
I found two 6-Ton bottle jacks on sale for $10 each and use one on each side (I got two to keep from carrying one back and forth) but NEVER lift both left and right sides at once, too easy for trailer to move thus kicking out jacks at 1/10th lightspeed while it falls. It's a three-legged table, always keep two 'legs' on the ground!
Is the 'Park' you mentioned paved or have concrete pads provided?
The tongue jack is really for hitching convenience - if the trailer is to sit for a while some timber cribbing under the 'A' frame would be worth the effort. Often the jacks are stamped with their load rating so that 1500
pound jack will self-destruct if you start using it to dead-lift the trailer w/o the usual counter-balance fore and aft of the axles assisting the jack.
I hope someones else chimes in w/ more info but DO ask if anything needs clarifying....