I think you're mis-interpreting/mis-using the backing plate. Particularly by using galvanized steel as the backing plate.
A few basics first. For any weld, the backing plate is used to substitute for the "back of the weld" on the root pass. After the root pass and first two cover passes, the "back of the weld" is the new metal already deposited, so there is no use nor purpose to a backing plate or purge gas in the pipe. The new metal is being deposited as melted steel/weld filler, so the melted and cooling steel need a purge gas/backing plate to ensure there is no "crap" (oxidized metal, dirt, contaminants, partially melted or partially covered slag, etc.) deposited inside the melt volume where you can't see it or grind it out.
Most important thing is to ensure the unprotected back of the weld is covered by something pure and uncontaminted and unaffectwed by heat while it is being deposited, while it is melted and before it completely freezes to a solid mass. Make sense?
Notice that the "front" of the weld is already protected by the SMAW (stick) welding slag or the TIG gas or the wire electrode coating and gas. A backing plate or back purge isn't going to do any good against contaminates or inclusions coming in from the front!
For regular hollow pipes using TIG or SMAW (stick) welding, we purge the back of the pipe with Ar or He gas or a mix or Ar-He gasses (because they are non-conductive, non-water-bearing, and non-reactive with the melted/cooling metal), then qualify the welder to fill in the gap with is root pass and cover passes without burning through new holes or the pipe walls. And without gobbing up the inside of the pipe with driblets of steel or unmelted weld wire.
A backing plate or backing ring can be used inside a pipe to fill across that gap and make welding easier, and to reduce the amount of purge gas and time of purging. But the backing plate is NOT part of the new pipe or new weld - is is just to allow the weld metal something to "melt against" to form the pressure barrier.
A loose backing plate doesn't do you any good: It still lets the contaminating air to get to the back of the weld while it is still melted. And, if the current loose backing plate is partially consumed while welding, then it can't slide out.
A dirty backing plate does you no good (and much harm) because it passes the dirt into the metal you're trying to keep clean, so I am very suspicious of using the galvanized plate. I understand the sq tube is NOT galvanized while being welded ??? True? (You can't weld galvanized steel without grinding off the galv coating first anyway. And even then the weld fumes are dangerous. Very dangerous if no grinding is done.)
SO, my recommendation?
Use a thick copper plate (1/4 to 7/16 inch thick) just under the width of the inside of your sq tube. It should be 10 to 20 inches long to absorb heat. Attach with rivets countersunk screws springs/spring steel/a bent plate to the back of the copper to force it up firmly against the inside of the sq tube walls.
Test by pulling the copper backing plate through your bent sq tube like a mandrell. When it goes through smoothly and several times, you know your fixture works. Then pull the copper plate through while welding right above the copper.