Former cold mill and pickle line technical assistant (process metallurgist) in a 1000tpd plant in the late 80's/early 90's when I finished my degree so knowledge is a bit dated.
Easiest option is the trial as mentioned above, but you need to find a way to measure it. While time at temperature is important in scale formation, my gut feel (and the 80's were a long time ago) is that there is minimal access to oxygen to form a scale layer in the middle of the coil that is much thicker than that which forms in rolling. The air would not enter the wraps of the coil as it heats and expands/pushes straight back out. I never worked in the strip mill and never had to worry about this - we ran a sulphuric acid immersion line, not a hydrochloric spray line.
1035 can form martensite if quenched too quickly, so I'd be guessing (and it is only a guess) that the coiling temperature would be 680-710C to avoid the knee of the TTT curve and your oxide layer problem would be hot mill runout table related. An increase of 10-20 degrees on the runout table would cause far more issues with thicker scale. As a gut feel, I'd start looking there first.
The scale, as you know, forms in three distinct layers, FeO closest to the surface of the metal, Fe304 in middle of scale layer and Fe2O3 on the outside of the scale layer. As the Fe2O3 is acid insoluble, you have to crack it to allow the acid access to the soluble FeO layer underneath.
I'm guessing that the problem is that the acid-insoluble Fe2O3 is building up in the tanks and/or transferring through the pickle line and entering the cold mill as a smudge layer on the surface of the steel, causing premature mill roll wear. There is obviously also the issue of increased acid consumption and decreased throughput due to the thicker layer.
If this is the case, I'd look to the scrubber ex pickle line to make sure strip is as clean as possible as well as trying to improve the amount of scale cracking pre-entry to the acid bath from the scale breaker to remove more scale early so the strip is cleaner.
You'll need immediate proof that the store-separately post strip-mill trial has worked rather than waiting for the sludge to build up. Do you have access to lab - if so, take 5 mid-coil samples from your current stock at the entry welder and measure scale thickness (micrograph) pre-trial, repeat post trial for another 5 coils. Head-end and tail-end crops are useless for this exercise. You may have a research lab associated with your company that has access to a SEM with glancing XRD capability or similar - if so and you need the proof, I'd look at the ratio of Fe3O4 to FeO in each sample to prove scale difference - I'm sure there's an old empirical way as well - be acid-insolubility for the woostite, haematite and magnetite.
Good luck with this - I'm expecting that the proposed trial will reduce scale buildup on the strip edges noticeably. Unsure on the effects on scale thickness across the width of the strip in the body of the coil.
