Will a short distance of small gauge wire cause relevant voltage drop?

When you are charging at full sun, you may see some loss in the cable. You have to weigh the options, thicker copper and less loss, or wait 20 minutes longer for charging.

Six inches of 14ga wire is not going to have a prohibitively high voltage drop, but at the same time you need to be sure even the short wire is capable of safely carrying the full expected current. 14ga wire is not usually considered capable of carrying 30A, but the actual current from the panel will be less than 8A. So that consideration is met too.

You're correct in being concerned about the long distance from the controller to the battery. The controller can be fooled into thinking the battery is at higher voltage than it really is and if so will transition from bulk to absorb too soon and potentially give you undercharged batteries. If you don't plan on adding more panels you should be fine with 12 ga. wire and as short a distance between controller and battery as practical. The short leads coming from the back of the panel are fine as they will only ever be carrying the current from a single panel.

Controller should be close to the battery so it sees actual voltage. When you say cheap controller, it is likely PWM and most wire losses won't matter in the least. You are loosing many volts between the panels power point voltage and the battery voltage. There is lots of room left over for wire loss. If it were MPPT and the lines were longer it might matter.Those wire tables are for loads where voltage drop does matter.

"Those wire tables" usually are for where voltage drop does matter as a percentage of 120 or 240 Volts. At 12V, however, the same absolute voltage drop is a ten times larger percentage of your source voltage. Hence even bigger wires are advised.

20' distance, 40 foot of #14 from solar panel to controller is 0.1 ohm. A 100W 12V panel is 5.5A. So, you get a half volt drop. With PWM you have 2V you can just throw away. You would not see any difference between #14 and #000 in this case.

If you can, get that controller close to the battery. It *does* matter.

Even with the above example of only 0.5v voltage drop, if you are charging a $$ Optima pure lead at 14.6v, and in reality are charging at 14.1v due to cable loss, then that expensive agm will always be a target for undercharge in a cyclic environment. You can quickly walk down your capacity that way. Oh yes, at some point like leaving it out for a few days, it will eventually get the controllers true cv voltage due to *eventually* charging to a point where current is low enough for loss not to be an issue - but in reality - your bulk charge and initial absorb stage will be much slower than desired and in a cyclic environment will be very inefficient.

Having a controller located on the back of a panel or close to it is merely a convenience, but not the right way to do it. Most controllers have at least "ambient" temperature compensation, and if you have your panel in the hot sun, with controller right behind on the other side, or quite near to it, the temperature difference between it and your battery located 15-feet away in the shade will be different.

Now the temperature-compensation is exaggerated at the controller driving your CV setting even lower, along with the seemingly miniscule 0.5v drop from cable loss - man it is easy to go down the wrong path.

Some of us have at times taken cable loss into account, and where it is just physically impossible to change the location of the controller close to the panel, have purposely over-driven the voltage as a kludge too. Don't do that either.

So yes, your original idea of getting that controller near the battery is a double-edged win-win for you if you are serious. Having the controller at the panel is just a marketing convenience, unless you also put the battery right behind the panel to have the controller and battery share the same ambient temperature. Hah, yeah, but no.

Your plan of moving the controller and battery away from the panel, and close to each other is the wise thing to do.