Thanks for the screenshots.. I can always pick up loads of info from them.
Your TC is correctly setup as router and the modem is pure cable modem and passing the IP correctly.
Keep track of the public IP as you will find some services change IP frequently and others can rotate them on a 3month or longer basis.. the longer the IP stays fixed the better. Hourly rotation makes it very hard.
Port forwarding should not be necessary.. as you say, you are using an all apple setup. IMHO the issue is that the Mac won't wake up..
Test it while you are at home. I want you to carefully follow these instructions so we can see if the problem is merely wake up.
Use your iphone on 3G tether or something (a friendly neighbour allowing you to access his wireless) so you can get a WAN access to your network when at home.. Then on your laptop that is accessing via WAN see if you can get access to the TC and the Mac... particularly see if the Mac starts up.. if it doesn't the issue has nothing to do with port forwarding.. especially if the TC is working ok over BTMM.. the problem is the Mac is simply not getting wake up messages. Or if it is getting the messages is not actually waking up.
If it fails to wake up the Mac.. go and wake up the machine.. and then see if you can access it.
Please tell me the results of this test as it will be pretty much the answer if I am right.
Only if the above fails.. ie even with the iMac running you cannot access it..
There is a couple of things I don't like. These maybe irrelevant.. but I would still like you to fix them.
I do not think 7.6.4 firmware handles the automatic port opening very well.. amongst other things.
I want you to try going back to 7.6.1 firmware. Just hold down the option key when you click on the version in the summary screen.. pick the earlier firmware from the list and allow it to downgrade.
Then I want you to factory reset the TC.
Universal Factory Reset.. any model TC or AE.
Unplug your TC/AE from power or turn off at the power point.
Hold in reset. and power the TC/AE back on.. all without releasing reset and keep holding in for about 10sec. (this is often difficult without a 2nd person or a 3rd arm).
Release it when the status light flashes rapidly. If it doesn’t flash rapidly you have missed it and try again.
Note..
Be Gentle! Feel the switch click on. It has a positive feel.. add no more pressure after that.
TC/AE will reboot after a couple of minutes with default factory settings and will wipe out previous configurations of the router.
No files are deleted on the hard disk in a TC.. No reset of the TC deletes files.. to do that you use erase from the airport utility.
Then I want you to redo the setup from scratch..
I want you to eliminate any name that is not SMB standard.. For instance your TC name is over long even for Apple OS.. See C9 here for why this is important. http://pondini.org/TM/Troubleshooting.html
Your disk share name is even worse.. the standard name is data.
SMB name.. short, 10 characters or less is excellent.. make it 20max.
No spaces. Spaces are very very bad.
Pure alphanumeric. No apostrophe.. that is also very very bad.
I want you to also fix the share name of the Mac. Change it from DANIEL'S iMac again to something that complies.. iMac would be fine.
As I said this will probably cause you plenty of pain and could well do nothing at all.
You don't need to do it all in one hit.. keep doing things step by step if you want.. but if it makes no difference then institute the next step.. changing the name of the computer will likely cause the backup to get lost so make that the last one.
BTW you stated you have the latest AC time capsule.. that is not so.. from your screenshots it is the older model.. and you could also therefore use the earlier v5 utility to see if the log of the TC will reveal anything about this issue. v6 utility is useless in diagnostics of problems.. v5 has at least got log access.
What OS are you running on your Macs??