I'm on Moogle as well and I seem to do just fine. Can I ask, are you a PC user on a console user? Because I'm both, and my experience changes dramatically depending on which I'm using at the time.

If I'm on the PC I normally have no problem getting to hunts when they are reported. My PC has an SSD on which the game is installed, which I think makes a massive difference. My teleport times are practically no different than normal on the PC. Maybe half a second difference. However, if I'm on PS4 then I experience the incredibly long load times that you suffer from as well. My PS4 still has the regular stock hard drive that it came with. It is harder to get to the hunts on time when using the PS4, especially for an S rank. But it is still possible.

What I would suggest is this:

1) Join as many linkshells as possible. I'm in about 5 hunt ones myself and can invite you to one if you like. It's not a big linkshell as it's my FC's one. But all hunts that I find myself get reported to that linkshell 15 seconds before the rest of mine.

2) If possible install an SSD into your PC/Console. It's not a cheap option I know, but it does make a massive difference.

Hope this helps.