Backyard Aquaponics
A place to discuss aquaponics

First of all, how important is it that I have a 1:1 ratio of Fish Tank to growbed. From what I understand, this is entirely dependent on the number of fish I have and how often I feed them.

Right now I have a 75 Gallon fish tank, but it's indoor, and I simply don't have space for a grow bed of the same size. What are suggested things I can do to help achieve that ratio?

One option is to make my growbeds deeper and increase their size that way, but I'm not sure if that would even matter. If I keep the number of fish in the tank low, could that help? Right now, my current plan is to add 3 of these as grow beds, but they are only ~7 Gallons each, so I am really far from the 1:1 ratio:
https://www.amazon.com/gp/product/B00VN ... UTF8&psc=1

you sort of answer your own question - what you have written is a pretty good summary.

use a drum full of media...the ratio is actually wet media volume to FT volume.
So you can have deeper beds or even deep pots of media.

the ratio is really a guideline and people have run 1:2 and 2:1.
As you note the critical relationship is number of fish to wet media.
But there is also the need for effective filtering.
So in first case keeping the fish numbers low will be fine.
As it is an aquarium you can also add other forms of filtering.

Your plants can be placed at the top of the fish tank as well.
And you can add plants inside the tank such as valisneria.

here is one option...

The volume ratio doesn't matter so much so long as you don't drain your fish tank when you fill your grow bed. A more important ratio for sizing is grow bed surface area to fish feed. Here is a nice calculator for several important ratios.

http://www.aquaponic.com.au/calculators.htm