The Guidelines Aren't Perfect
Custom Magic Item
3/day Swift Action Speed
Long Arm (Spell Level 1, Caster Level 1)
Duration 1 round
Let's say you want the pricing within the guidelines for the above item.
\$(\text{Spell Level } 1)(\text{Caster Level } 1)(2000 \text{gp}):
2000\text{gp base cost}\$
\$\frac{\text{3 Charges Per Day}}{5}: 60\% \text{ price factor}\$
\$\text{Emulates Spell with Minute/Level Duration Normally}: 200\%
\text{ price factor}\$
Base Cost: \$2000\text{gp}\$
Total Price Factor: \$120\%\$
Total Price: \$2400\text{gp}\$
You were off by a factor of two, but you've pretty much got the price of the item from the guidelines that exist.
Things not priced in because there is no guideline:
- Swift Action speed of activation.
- Intuitively would cost more due to Use-activated cost being used in above equation. Use-activated is at Standard Action Speed.
- One round duration of effect.
- This should make the item cheaper in some way as following these guidelines you're paying for Caster Level 1 charges which each should last 1-minute long.
How could we price these in?
Pricing in Swift Action activation is somewhat vague, we could price the item higher by making it require the use of Quicken Spell, which increases the Spell Level and Caster Level of Longarm in the equation to SL 5 and CL 9, which multiplies the price by a factor of 45.
Adjusted Price: \$108\text,000\text{gp}\$
If you look at Boots of Speed, they're priced at CL 10 and 10 charges/day (1 round of the 10 rounds per charge) activated at Free Action speed. Free Action speed is better than Swift Action speed, and it has no price modifier.
Adjusted Price: \$2\text,400\text{gp}\$
Of the two, the first is completely unreasonable while the second one seems like we're getting something for free.
As for the 1 round duration, we could think of it similar to the Boots of Speed again. Caster Level 1 Longarm gets you 10 rounds of the effect, of which you're only making use of 1 round. It would be reasonable to say that you would price this custom item at a 90% discount since you're only getting 10% of the time.
Adjusted Price: \$240\text{gp}\$
That's far too cheap. Unacceptable at many tables. Reasonable logic lead us to an unreasonable price. Go figure.
Let's say that we apply both options at once, then. Longarm at CL 9 (to allow for Quicken Spell) is 90 rounds of the effect, so you're getting 1/90 of the effect.
Adjusted Price: \$1\text,200\text{gp}\$
VERY interesting. If we follow both of those logical trails, we end up at what your original estimate was (which was half of what the guidelines recommend). However, this is still six times less than the Longarm Bracers' book price.
Guidelines are guides not absolutes
As you've probably read in most places pertaining to creating Custom Magic Items,
The correct way to price an item is by comparing its abilities to similar items (see Magic Item Gold Piece Values), and only if there are no similar items should you use the pricing formulas to determine an approximate price for the item If you discover a loophole that allows an item to have an ability for a much lower price than is given for a comparable item, the GM should require using the price of the item, as that is the standard cost for such an effect.
Paizo has indicated that 7,200gp is the standard price for an item granting this effect. They generally base these prices on the guidelines, but also sometimes on levels at which these abilities should be available.
For example, these Bracers grant a comparable effect to Lunge (Combat Feat). That feat is only accessible at Level 6 by Full BAB characters. The expected wealth of a Level 6 character is 16,000gp. Pathfinder expects that no player character will have an item that is worth over half their total wealth. Level 6 is the level at which the Longarm Bracers fall within that margin of acceptability.
This is one, but not every, reason why magic items might be priced higher than their guideline estimates.
Getting back to the questions at hand
The title question is "Is this custom Bracers, Longarm correctly priced?"
You're technically off by a factor of 2 according to the third step I listed at the top.
"Is it balanced?"
Not particularly. Even following the corrected price of 2,400gp, you're getting a magic item as early as level 4 that emulates a 6th-level feat. If it required you to be a spellcaster to use it, maybe it could be priced as granting three bonus casts of Longarm per day, which is about 3,000gp (priced at pearls of power). Even then, it's kind of iffy as there's no guideline for this sort of deviation from the Longarm Bracers.
"Is this custom Bracers, Longarm correctly priced?"
Again, not quite.