I have twenty 12V, 100W panels mounted on a custom trellis overhang, which provides shade to my vegetable garden plants. These trellises are spread out along the rock wall in my backyard. My idea is to connect four panels in one string (48V) and run those lines to the string closest to the house. The farthest string will have about a 100' run, and that's where I plan to place an outdoor combiner box.
OK, you are making some mistakes here. Very most likely, your four 100W panels will NOT be putting out 48V. It's called a 12V panel because it's used in 12V applications, NOT because it's output is 12V. You also pay a price premium for going with panels designed for automotive use. You would have gotten more W/$ if you had instead purchased larger high-voltage residential grid-tie style panels.
Flip a panel over and look at the nameplate on the back. You will see values for Vmp, Voc, Imp, Isc. Please refer to those as your operating values. Most likely, one panel will have a Vmp of ~18V, and a Voc of ~22V. These numbers are VERY important in the proper design of your system. The Voc is what you pay attention to when you are deciding what size string to feed into your controller. Don't decide on how many panels you put in a string until you know the specifications of your electronics. Some controllers have voltage limits down at 100V. Some are 450-500V. You have to know first what you are working with. Controllers also have minimum voltage requirements, below which they don't work properly. You need to do more research here.
BTW, four panels in series might have a Voc of 88V, but that's at room temperature. As the panels get colder, their voltage goes up. That 88Voc, will likely bump up past 100V slightly below freezing. So, the first frosty morning will fry a 100V limit controller.
The good news though is that the voltage drop for four panels in series is not as bad as I expected. Assuming each panel is 18V, so four is 72V. Here's a voltage drop calculation to show how much power you are losing at 100'. Not too bad.
You can play with this drop calculator yourself, as you gain more details about your proposed system.
This free voltage drop calculator estimates the voltage drop of an electrical circuit based on the wire size, distance, and anticipated load current.
www.calculator.net