I could be wrong but I believe the humming is a result of the transformer doing what it's suppose to do. As it steps down the current from 120v to 12v, there's interference which generates the humming. (So I think.) Anyway, what you need to be conscious of is that the transformer isn't overly hot. Kichler Lighting is who manufactured my outdoor lighting. With the lighting system, I got a great installation booklet on where and how to do this job. It gave the formula to determine how much of a transformer you'd need, which way to run wiring, it described voltage drop, and talked about future expansion. I installed out transformers in our basement stairway in the house. (I drilled through 11" of poured concrete to get the wiring inside!) Our hum is slight. Although the transformers were rated for outdoor installation, I opted to keep them inside. It's easier to change the on/off timers for Standard and Daylight Savings Time. (I don't have a photovolcaic system because we don't want the lights on all night. And that's why I put them inside too.)
I guess the answer to your problem is to move the transformers to another spot. You'll have to refigure and recalculate for voltage drop if you end up adding wiring to the existing string. As an aside, I soldered my connections even though it's not necessary. I then used a Tub & Tile caulk to 'protect' the connections. I then used a shrink-wrap tubing that can be bought at any Automotive Store like Pep Boys, NAPA, or the like that's shrunk-on with a hair dryer. THEN, I buried the wired. If you want to go this route, e-mail me directly and I'll give you one last tip. I'll spare you here because you may have already done your installation. DON'T wrap or cover up your transformers as the heat needs to get out. It's a by-product of the step-down process. There are transformers that you can buy that do a better job of insulating the unit for you. Try Vision Info Soft. Search the WEB page for the word 'hum' using your Browser's FIND feature. When you find it, scroll up a little and you'll see a full description of the item.