So, after some tests in various conditions (where I auto-disciplined myself into only having the maximum number of Stainskip my GG amount would normally allow), I'll try to give a first opinion on the civ balance-wise.
First and foremost, what I like about this civ is that is has, beneath the apparent simplicity of a large part of its kit, a big amount of innovative concepts (aside from the obvious resource requirement for the UI) :
- This is the first civ in VP to have both its UUs require strategic resources (Japan doesn't count, since the second UU comes during the very late game, while here the two exist simultaneously)
- This is one of the only civs in VP to have both UUs with almost no base CS modification (which usually takes a bonus slot design-wise), and so in exchange powerful promotions that are not lost on upgrade. Because of this, the civ has a smaller but very long power spike beginning the Classical era.
- Each of the UCs of the civ are long-term bonus that scales with you throughout the game : the UI gains a lot of yields through techs, the UB gives more and more yields when you increases your Unit Supply cap, and as I said the promotions of the UUs aren't that impressive at first sight but provide a strong base for very powerful units later
- This warmonger civ is tailor-made to bring down developped civs by using their infrastructure (roads, pillage) and gaining more yields when conquering big cities.
All of that said, there are some problems in practice :
- The road bonus of the Foederati promotion is, in the end, far less powerful than one could imagine, simply because the AI nowadays knows well how to surround and destroy any out-of-place unit, and so what was a very strong bonus in base Civ V is here a lot less usefull, even more when the kit tends to emphasize big unit lines where the durability of the Gadraught and the ability to focus and destroy of the Groethungi Cavalry make more sense.
- The fact that the Stainskip is available so early is actually a sort of trap for the player : until the late Classical era, the Goths don't have the military to be able to begin conquering (at least against Emperor+ difficulty), and so trying to conquer and pillage is actually quite risky (for the "Foederati" promotion doesn't give the same early edge as the "Viking" promotion of Denmark for example). Thus, quite counterintuitively, I actually advise against taking Bronze working early right now (except if you really want some Spearmen) and go more toward gold and science buildings so that you don't fall behind science-wise, since it's one big weakness of the civ's kit, until you get ready to become agressive.
- All of these elements acknowledged, there is one more problem linked to the UUs this time : as I said above, the Goths are a civ whose two UUs require strategic resources. This wouldn't be a major problem in itself if both units brought immediate power to the table, but, as I tested more and more both units, I realized that none of them had the "oompf" that at least one UU in each civ's kit has : the Gadraught is durable, but not as the same level as the Legion for example, and is the weakest Swordsman replacement I know offensively ; the Groethungi Cavalry has a lot of offensive power, but is itself quite easy to kill, especially in the type of battles its unique promotion normally favors (line vs line wars).
=> The interesting effect of all of these elements is that, to me, the Goths are a civ with all its UCs coming early on, but whose power spike comes far later, when the UCs of the Goths start truly scaling, kept unique promotions start to shine (versus the UUs of other civs, which always lose a part of their power when upgraded) and the UA gives you tangible bonus (improvements to make Foederati useful, base yields in city to make the bonus-on-conquest truly noticable). With that in mind, I imagine a lot of players will be frustrated when playing this civ, since it seems to encourage you to do early-warmongering (plus, it's the Goths, so there is a cultural bagage here telling you to conquer during the Classical era) but in the end doesn't give you a kit truly efficient in helping you that way when compared to other warmongering civs with early UCs.
What solutions could there be ? Personally, I like the fact that the Gothic unique units don't have additionnal base CS (or weak ones in the case of the Gadraught) and the general idea of the civ's kit, but some little buffs could be made :
- For the Gadraught, an economical bonus could be added I think to compensate for their weak stats compared to other Swordsmen UUs. Your historical description for the unit says that it was more akin to informal warbands, so making it easier to mass could be an interesting idea, maybe in exchange of the +1 base CS ?
I'm throwing ideas on the unit card here.
Gadraught
Unlocks at Iron Working
85
Production (instead of 100)
Requires Iron
or Grave Goods (don't know if that's feasible)
2
Moves
17
CS
Thervingi (+15%
CS in Rough Terrain. 25% Damage Reduction from Cities)
Drill I
Cover I
- For the Groethungi Cavalry, the fact that it is unlocked in the Medieval era unit while historically having seen its glory days in the late 4th century AD is a bit strange. It propose here that the unit become available at Metal Casting and is also a bit cheaper, in exchange of 2 or 3 base CS (the strength of the unit is base on killing strikes anyway, so having a bit less defense isn't that important).
Example :
Groethungi Cavalry
Unlocks at Metal Casting (instead of Chivalry)
160 Production (instead of 200)
Requires horses
4
Moves
21-22CS (instead of 24)
Can move after attacking
No bonuses from Defensive terrain
Reduced penalty against cities (only -15 % CS) => To compensate for lower base CS
Reinforcements (+10% from flanking. +15%
Strength against a unit for each attack it has already taken this turn)
- Finally, a additionnal bonus to the Foederati promotion could make it more useful early on (had an idea linked to ZOC, but that would be too similar to the Carthaginian UGP)
These modifications wouldn't make the Gothic army more powerful in the long run, but would give it the means to be a real power during the time it is supposed to be (however, the strategic resource requirement would force you to expand early to secure these resources).
For the idea of the Grave Goods-requiring Gadraught, a solution here could be to create a separate UU with the same stats and arts, but I think other more simple solution could be found to make the unit easier to mass.
Culture and 
Capital triggers a 
Golden Age.
2
1
War Supply on Empire
Population before capture.
