FemJock, it seems you have a nutrient/light imbalance in your tank that needs to be addressed at a fundamental level (less light, fewer fish, smaller feeds, etc.), but the most tractable solution to the immediate problem of a diatom or bacteria free-floating bloom is a Vortex Diatom filter. Have you tried this yet? They're a bit old school (note my join date <-- ), they're not cheap (~$130), and they're hard to come by, but those things work better than any other filter that I know of for addressing blooms, and you can see it has worked in 10-20 minutes. The diatomaceous earth is porous, and the algae get trapped in there. Running the filter for ~24 hours clears enough of the algae to really beat back the bloom for good if the source of the bloom is eliminated. Many other filters may get some of the algae or bacteria out, but enough remains that the bloom re-establishes itself. Not sure if links are allowed nowadays, but here's the link to the Vortex website if so:
Diatom Model "D-1" Filter - Vortex Innerspace Products Inc.
Another relevant point is your tank size and fish load. I don't see a mention of your tank size, but with the number of fish you have, I'm hoping you have something relatively large. An old rule of thumb is a limit of 1" of fish per gallon of tank for freshwater. This holds true relatively well for small fish (<4", say) in freshwater settings, and can be bent if you have lots of plants that suck up nutrients, but it falls apart for larger species where biomass and length don't scale linearly (e.g. an 8" Oscar is has probably 20-100x the mass of 8 1" Cardinal Tetras). From your description, I'm guessing you have ~20 fish, some of them at least 2-3". If so, you may be over the bioload for a small tank, and you may want to consider returning a few to a store, or starting up a second tank to house them.
The problem with blooms like you describe is that they can be singularly persistent, even when you've addressed their source. If money isn't an issue, buy the Vortex Diatom filter (smallest size, above, should be fine), and simultaneously address the bioload issue if relevant. If you want to avoid the cost, call around your LFS (local fish stores), especially those that seem to specialize in fish (not Petco, PetSmart), and ask if they rent their Vortex out. If they do... that'll save you a fair amount of money, but you'll want to make sure you soak all parts in bleach beforehand and after to ensure you don't end up getting Ick, or the like, from the filter. (I really don't recommend this option, but hey, it's out there.)
On algae eaters, you'd do well to check on the species you have. Some are great; some not so much. Avoid so-called Chinese Algae Eaters (
https://upload.wikimedia.org/wikipe...cheilus_(Chinese_Algae_Eater)_in_Aquarium.jpg ) like the plague. They get huge, and the bigger they get, the less well they clean algae, and the more aggressive they get. Favor so-called Siamese Algae Eaters (
http://jurnalaquascape.com/wp-content/uploads/2015/10/SAE.jpg , note the pointier nose, typically clearer line on the side) if you're confident you can keep the tank in good health. Avoid standard plecos (often look something like this, and are cheap:
http://aquariumtidings.com/wp-content/uploads/2014/06/Plecostomus_700.jpg and can reach 2-3 feet in the wild, usually ~8" in a tank), favoring bristlenose plecos (
https://www.keepingtropicalfish.co.uk/wp-content/uploads/2012/01/bushy-nose-plecostomus-500p.jpg https://aquaticmag.com/wp-content/u...co-for-sale-and-where-to-buy-AquaticMag-8.jpg ), that tend to reach ~4", and which are dedicated algae eaters. They used to be quite expensive, but they breed *very* easily, so they're now a common presence in fish stores. Corydoras catfish (many varieties, but note shape here:
https://d11kavc4axrfgm.cloudfront.n...ploads/1970/01/29103628/corydoras-catfish.jpg ) are good general bottom cleaners (benthic/benthopelagic), but they're not great at getting the sides of tanks, so they're not a good choice for beating back serious surface-blooms.
I've experienced all these issues before, and one of the things that drove me away from aquariums for so many years was the degree to which many stores gladly, almost gleefully sell fish to unsuspecting customers, knowing that chaos, blooms, death, are on the horizon. It affects their bottom dollar too much to only sell appropriate species for stable tanks... I get it. But it nips enthusiasm in the bud so quickly when your tank dies off...
Good luck!