In my youth on the Navajo Reservation while runnng first the Teec Nos Pos Texaco and later the Shiprock Shell Station, I think I've seen it all when it came to tire patching, jimmy rigging and working without proper tools in general. We even did truck split rims with curved chizels, tire irons and a sledge hammer. Whew!
We hot vulcanized inner tubes in those daze! Tubeless was new then. That'll date me.
The jack base will probably work and won't generally hurt a tire if it doesn't have a really sharp edge.
You can even try popping one by jacking your Jeep up and put the rubber of the wheel under a tire and jack the jeep back down on it. If the vehicle mounted wheel has a decent edge on it, you can pop a bead that way sometimes.
I've even poped them by rolling over the rubber ... but it helps to have a spotter do do this ..
The edge of a bare rim on the vehicle lowered on the bead will work every time!
You will need two or three tire irons and/or big screwdrivers to pry and pull the ID of tires off the rims after you break the bead.
It doesn't hurt to have a BFng hammer and a little soapy water on hand either.

BTW: The classic "tire iron" .. you know, the dog leg shaped bar with a lug nut socket on the short side and a screwdriver shaped flat on the other...that came with most pre '80's vehicles ...
And you just always thought that end was just used to pop the hub cap ...
The specifically designed tire irons also are flattened but have a 'wave' in them to help you get the end of the bar under the lip of the bead.

JAF
http://www.monsterslayer.com/jeep

 

the hi-lift will work. you will probably have to do it in two different places before it breaks.

brian wilson
80 cj5 "high 5"
stretched to 100" wb
351w/np435/d300/d44/d60/detroits/4.56/35ss/bdlocks

 

Drive over the tire - works every time...

Chuck Hadley