Arms, the SLAM mantra may sound prescriptive, but there's a reason for that. Complete oxidization of the water, accomplished by the "maintaining" part of the slam at (slightly above, actually) the correct (for one's cya) level, actually does make the water crystal clear to a level many don't realize -- eg. seeing the detail of a quarter on the deep end! Even with sediment. As you know, I had a ton!
It's not just about staving off algae...its about sanitizing the water to a truly safe level and ergo being able to go forward in a truly "trouble free" way
(Although it should be said that "nascent" algae first turns up as cloudiness in the water, not sudden visible green, and many people who have cloudy water are actually just riding the line on not-quite-sanitized water...not saying that's necessarily going on in your case with the particulate, but it could be contributing to your cloudiness.)
In your case, you changed the water, but are still dealing with the stuff that had clogged your lines, which will have been full of pathogens. Algae or not, I'd sure like to feel comfortable that you've beaten it down
While i understand why it was important to address your filtration issues, had you slammed then it would not have been the waste you think. Once your water had achieved complete oxidization, your chlorine demand would have dropped dramatically -- so if you HAD been slamming fully the last few weeks, the level of chlorine required would have followed a downward curve to a place where your daily dose would be much closer to normal maintenance anyway.
Eg. In the last few days of my swamp conversion, you may recall from my swamp pictures that the water was crystal clear and showing a pile of leaves in the corner
even with those leaves in the corner, I didn't have to add more than a jug of 6% to keep it above slam level...and my now "normal" use age is 2-3 ppm per day -- about the same!
Now that you have a working filter and a comparatively minimal amount of debris, your Slam -- if you maintain above slam level at all times and don't let it drop -- should be short work and give you a great baseline for a trouble free future in pool ownership. If its done correctly and you follow the cya:chlorine chart (see my sig) from here forward, it should be the last slam you'll ever have to do
That's the point of the "mantra." It's just what reliably works!
Going forward, post a set of test numbers and bring your ph to about 7.2 for optimal pre-slam conditions. In general, you don't need to worry about TA until everything else is well in hand.