I jack from the pinch welds all the time.. some people cut a slit in a hockey puck to protect it from a regular floor jack.. there's also a product out there for this purpose:
Amazon.com: Universal Slotted Rubber Jack Pad Frame Rail Protector: Automotive
^This, I use the hockey puck trick often. I wouldn't waste my $ on the Amazon ones though; you can buy 4 hockey pucks at any Walmart for that price & cut the slits yourself easy enough. A finish router with a 3/16" or so bit cuts a perfect slot very quickly.
Those side rails really are tinny, they always seem to bend on any car that needs to be jacked up these days. I'm forever having to bend them back into shape. Some people don't bother, and just leave them bend over. I don't like the look though. It's a pity the manufacturers don't strengthen them up a bit. But I suppose it's all about super thin bodywork these days.
They pinch welds are very flimsy, and often smashed in. What I did on my RX7, after straightening out the smashed pinch welds (bought car used), was to build up "hard points" for jacking. Took short lengths of 1"x1" solid AL stock, cut a slit along its length just thick & deep enough to fit over the pinch weld, and then epoxied it to the pinch weld. Now I have 4 solid points to jack from, which are basically the stock ones, just beefed up (spreads the jack force over a larger area - pinch weld and surrounding structure) and easier to position a jack or stands under.
I believe I found a solution for lifting the Mazda three to get jack stands on the car, and an obvious solution is to use the other lift points under the center of the car. But the front one is so deep under the car I cannot see how a hydraulic for jack can reach it. I searched for long reach floor jacks I did not find one I thought could reach far enough under. If anybody finds one that can, please let us know.
I have this Harbor Freight jack, see link below. Works great on my RX7 (also a long reach) and my '3. Only catch is to get that reach, you'll have to start it with the lever almost horizontal to clear the front bodywork, laying on the ground to position it right & get it started. Once you position it, takes a few "baby pumps" till the handle will clear the bodywork, and then you can get off the ground and pump it up the rest of the way easy-peasy.
2 ton Low Profile/Long Reach Steel Heavy Duty Floor Jack with Rapid Pump®
The other thing I will do is the next time the car is up on ramps I am going to locate that center jack point and spray paint it a bright color so it will be easy to see and spot.
^I like that idea, would make the job a lot easier!