Lindens, little leaf in particular, have their own species of aphids that will infest the trees seasonally. Extensively planted as street trees in London, they are in the process of being systematically removed simply because of this problem - sticky honeydew being dropped onto parked cars and passersby. To the best of my knowledge, ants farming aphids are a restricted to only certain species of aphids, therefore I'm not sure you will accomplish much by restricting the ants, especially since they have not yet been apparent on the tree so far. Spraying the tree with a strong stream of water is probably your best bet for control with minimal side effects :-) It serves to dislodge and even destroy the aphids as well as washing off the sooty mold. And easy to do with the frequency required. Insecticidal soaps can work also, but you have to actually coat the insects to effect proper control and you've already determined the difficulty of that with a 35' tree! And insecticidal soaps can create a phytotoxic situation if the timing is not considered properly. Systemics can certainly help. Bayer produces a tree insect systemic that is quite effective against sucking insects like aphids. It is an imidacloprid-based product and is quite toxic to bees but if used as a systemic, relatively harmless to anything other than sucking or boring insects. Not sure that I'd consider systemically treated fallen leaves as 'poison bombs' - just as harmless and compostable as any other untreated leaf. Remember that this will be an ongoing battle :-) If you want to keep the linden, you will have to deal with the same problem every spring.

I'm guessing you have the Safer brand RTU product, which is expensive and tedious to apply. I have used Bonide (or other brand) dry micronized sulfur applied with a tank sprayer, with a little soap for a spreader-sticker. It is quite effective vs. PM and somewhat against blackspot. Sulfur is safer to handle than copper products. If you want to switch to a synthetic chemical, go to Lowe's and look for Bayer Rose, Flower and Shrub Disease Control (that exact name). It is effective if applied every 10-14 days.

No - sulfur does NOT leave a white deposit. It is clearly yellow. Rub a small amount of the residue between your fingers and see if it is actually yellow. .Sulfur relies on that residue to work - don't wash it off. The product you used is a flowable sulfur. It is effective against PM if used properly. You must use it at the recommended 7-14 day interval during the entire time PM is active. If PM is a major problem or if it rains, apply at the 7 day interval. If using a hand sprayer, be sure to keep agitating it while applying the sulfur. One issue with sulfur is that like any other protectant, it washes off due to rain or irrigation. Another issue is that sulfur may cause plant damage if it is on the leaves in hot weather Finally, sulfur reduces the predatory insect, mite and spider population. Those predators help to control damaging insects and mites. I'm not saying to not use it, but keep those issues in mind. We've stopped using sulfur for PM control and now use a potassium bicarbonate product (Green Cure). It also has to be applied at frequent intervals to control PM, but it has fewer side effects.

What type of fungicide? What do the directions say? I use Safer brand which is sulfur and it will leave a (light)residue, but I mix according to the directions which I think is 1 or 2 tablespoons per gallon of water(don't have the bottle in front of me). If you used the proper dilution I wouldn't worry about the residue. If you think you overdid it you can keep an eye on the plants for damage, or rinse it off and reapply if needed.