Have to agree with you
The jacks used on the newer trailers, are by and large junk. Fortunately, on the 2008 I had sturdy BAL scissor jacks that were quite adequately attached and I never needed anything more. A friend of mine had power jacks on his FunFinder and we ditched those and installed BAL scissors (manual) in place of them. I've never been a big fan of the motorized scissor jacks; either the motors are too weak and the jack winds up being less than effective (as in your case) or the motor is strong, too strong and the user winds up tweaking the frame. Then you run into the "motor just quit on me last night..." syndrome.
Give me a sturdy pair of manual jacks; I don't even need a drill. I use an old fashioned socket brace (a "speed-wrench"; hard to find nowadays) and a socket bit. Nice ball bearing hand grips, easy to spin and a lot of torque, much better than the "speed wrench" that comes with the jacks.
Now to your situation... His was a lot like yours...easy to put the new BAL scissor jacks on the front, lots of room. In the back was a story similar to yours. IIRC, we wound putting some angle iron kitty cornered across the back from the frame to the "I" spud that the bumper was welded to. We could then mount the BALs to that and the frame. Seems to me the mounting base plate of the BALs that we used was ~4" long. That was a couple of trailers ago for both of us, so I may be "confused" about the baseplate width, but, it was either using the span plate (angle iron) or we'd have wound up with a weak attachment point.
Edit: 12/2 I remember now why I didn't need braces on my 210WBS. It had the BAL "C" type jacks on it...if you look at the design of them, they have a "built in" diagonal brace between the leg and the frame; served much the same purpose as the Steadfast or StrongArm type bracing and all four of them were mounted "kitty cornered" across the frame corners (diagonally; not a single one was aligned with a frame rail). That made the jacks push against each other diagonally across corners. We couldn't get those to fit on his trailer due to the tank positioning. If you look at how a scissor jack is built, it has a single contact point at the ground (the foot) and a single contact point at the frame which gives you two pivot points. Not as stable a design, much more compact and easier to find a frame point to mount to, but, inherently not as stable. The same thing I have on my 5er and, IMHO, the reason I'll probably wind up either changing them for the "C" type jack or I'll have to put the Steadfast system on it in order to get "stable".
As for cross braces? They, by all accounts work, but, on my FF, I never felt the need for the cost or the extra work in setting up the trailer that they entail. In order for them to be most effective you need to put the stab jacks down (after loosening the cross braces), then tighten the cross brace handles then go back again and put some additional tension on the stab jacks to "tension" the whole affair in order for them to be "at their best". Of course, they are an extra step in packing up, too. Along those lines, I have looked into them for my 5er; much longer and heavier and I can definitely benefit from the additional bracing with this trailer. I'm a minimalist and the fewer braces that I have to fool with the better and I've decided on the Steadyfast system. Uses only three braces as opposed to 4, 6 or 8, the handles are much easier to get a grip on (no wrench required, either) and I've yet to find a bad "review" of them or their company. Still haven't decided if I'm going to go the "brace" route or just deal with the little motion we have; there's only the two of us and it isn't like we a boatload of kids running around the trailer, so, I've yet to decide if the extra setup and breakdown steps are worth it
If I were you, I'd go the better jack route first and see what you've got; you can always add braces later...