I ultimately was not able to resolve the wiring problem given the current set-up and the wiring in place.
However, I did end up purchasing two sets of https://www.amazon.com/RunLessWire-Simple-Wireless-Switch-Kit from RunLessWire directly ($99.99+s/h each), linked both wireless switches to both relays, removed the existing switches and shorted the appropriate wires, and 2 hours later, I had a working set-up!
OK, here goes:
What you have now
The power from the panel seems to come in in the middle of the bottom of the box. That black wire is always hot, and is connected to all of your switches via the orange nut you labeled e, which connects wires d, g, i. i connects to j via switch 3, and j (which is the same as m) connects to the always-hot (k) via switch #4. You shouldn't use the side screws and the backstabs at the same time (you shouldn't use the backstabs at all), especially since it looks like those screw terminals will accept two wires each.
a, f1 (f3), L, and h all look to be switched-hot, and will only be powered when the corresponding switch is in the 'on' position. L is a little troublesome since you said it only controls 1 fan, yet there seems to be 2 wires there. A clearer picture of switch 4 might help.
What you need for the new dimmers
Essentially, keep what you have. Each switch gets wired to the always-hot via a black wire. You can run a pigtail from each switch and nut them all together with the always-hot, or daisy chain the always-hot from one switch to the next. A lot of switches and dimmers come with pigtails already, so that's probably the easiest. If you do daisy chain, use the screw terminal for both wires, unlike how it's wired now.
All of your neutrals (white) get nutted together. There's a big bundle of neutrals already nutted together in the back of the box. Your new switches may require a neutral, in which case you'll need to tap into that big bundle. Given that there's already 5 wires in that nut, you'll probably have to separate it into 2 or more bundles and pigtail them to each other. Or use some large (8-port) push connectors instead of wire nuts. If your new switches don't require a neutral, leave that big bundle alone.
All of the grounds get nutted together as well. It looks like none of the switches currently has a ground attached (which is a no-no), so you'll need to add pigtails for those, and bundle them all together. Make sure at least one pigtail remains attached to the metal box, as well. Looks like you could pigtail the grounds for all 4 switches together with a pigtail to one of the screws on the box behind switch 4, as the rest of the grounds seem to be attached to the box already.
Finally, your switched-hots (a, h, f3, L) need to be connected. Get some electrical tape, and tape those wires with red or blue (or something other than white or green), so you can easily identify them in the future. Attach each to the corresponding switch. If there are multiple wires, use a pigtail and wirenut, or put both into the screw terminal (if the terminal supports it).
Best Answer
You now have them correct, the one good thing with 3 wires connecting the 3 way switches you don't have to worry about burning things down they just don't work as you found out if they are wrong. Good job of figuring it out, you would not believe how many times I have been called to do what you just figured out.