If you are proficient in an exotic weapon then effectively you have exotic weapon proficiency (that weapon). I can't imagine you'd need to get the feat separately.
The FAQ's there to prevent the exploit it names (trading armor proficiencies for other feats). You aren't trying that kind of exploit. Their reasoning is an attempt to deny that the exploit was ever possible, and it's kind of embarrassing.
Very strict RAW, you need the actual EWP feat. But RAW and proficiency feats are natural enemies, as these are literally the worst written feats in the CRB. I'm not exaggerating when I say that I don't think there has been a single table in the history of Pathfinder that actually used these feats fully RAW. Because that way lies only madness.
The main issue is that none of the proficiency feats actually grant proficiency. It's all they should do, but not one of them does it.
• Simple Weapon Proficiency says "You make attack rolls with simple weapons without penalty.", which has the same issues as Shield Master because it doesn't say which penalties.
• Martial Weapon Proficiency is fairly accurate because it specifies that you make attack rolls "normally (without the non-proficient penalty)".
• Exotic Weapon Proficiency says "You make attack rolls with the weapon normally.", which could mean just about anything or nothing (including ignoring underweater penalties, for instance).
• Shield and Tower Shield Proficiency work comperatively well, as they make it clear you only get the ACP on skills.
• Light, Medium and Heavy Armor Proficiency don't do anything as written, because they all say "When you wear a type of armor with which you are proficient, the armor check penalty for that armor applies only to Dexterity- and Strength-based skill checks." That just repeats the general rules, but the feats don't say they grant proficiency...
The fun doesn't stop there, because someone considered it smart to make absolute statements as supposed reminder text in the special sections. For instance, SWP says "All characters except for druids, monks, and wizards are automatically proficient with all simple weapons." Guess that meany my Shifter is proficient with more than what the class says? Also, "All characters except monks, sorcerers, and wizards automatically have Light Armor Proficiency as a bonus feat.", this would be good news for a With or Arcanist, if light weapon proficiency actually did something.
The FAQ that you quoted explicitly clashes with some of these special sections, e.g. HAP's "Fighters and paladins automatically have Heavy Armor Proficiency as a bonus feat.", yet there is no mention of a future erratum or anything.
Bottom line: Treat #1) Every prereq of a proficiency feat as asking for the proficiency, and #2) every proficiency feat as granting the respective proficiency, and nothing else; ignoring most special sections.
While it doesn't say you get the feat saying that a character who isn't proficient with the weapon via the feat but other means would be the same as saying class armor proficiency doesn't qualify you for the higher level armor prof feats..
Any GM that rules against the proposed build should be asked if a fighter qualifies for weapon focus: long sword. Tableflip in response optional.
I looked at that but Weapon focus doesn't require the Feat Martial Weapon Proficiency it just requires you to be proficient.
Sorry if I'm being a pain about all this.
You aren't. If I came across as annoyed or anything, it's at Paizo for totally screwing up and never fixing it, not you!
Because re-reading what I've wrote feels very unclear, my bottom line #1 is supposed to read "Treat every instance of a proficiency feat being listed a prerequisite as if mere proficiency was listed, instead". Chain Mastery's prereq should be interpreted as saying "Dex 15, proficiency with spiked chain."
If you are really worried, you might make your character a Half Elf instead of a Half Orc. Instead of Chain Fighter, you take Ancestral Arms, Spiked Chain, and you have straight-up Exotic Weapon Proficiency with the Spiked Chain.
Well, if the GM is really being a dick about it, that doesn't help, because a Gloomblade can only create weapons they're proficient with, and as detailled above, the feats don't actually grant proficiency (per strict RAW).