[OMFG!You'reActuallySmart!]

The most similar medication to gabapentin would probably be pregabalin and is more potent than gabapentin as well as newer. To treat an anxiety disorder, there are several options in terms of what types of medications.

One group of medications that can augument SSRIs while treating anxiety and sometimes acting as an anti-psychotic is the azapirone class. In particular, from this class: tandospirone (used to treat cognitive impairments from schizophrenia), Buspar (not very potent and researchers aren't in agreement whether it can improve cognitive impairments), eptapirone (very potent with minimal side-effects) and Lullan (anti-psychotic as well as anti-depressant and anti-anxiety). They could treat the depressive aspects of the rapid-cycling and possibly reduce anxiety during the manic phase but not reduce the manic phase itself. All have a very short half-life and work pretty fast.

Another class of medications to treat anxiety but will produce some sedation (intensity will vary per medication) and muscle relaxation are benzodiazepines*. However, unlike the above list, benzodiazepines have a much longer half-life, so you may not need to take many pills in one day. For example, medazepam has a half-life of up to 200 hours, whereas azapirones have half-lives less than 5 hours. Although 200 hours seems a long time, some other benzodiazepines have up to ~250 hours (did not list those because they usually are powerful sedatives) but the others below have half-lives at a MINIMUM of around 20-40 hours. Ones that have few cognitive side-effects are Ativan**, Xanax, Bromaze (powerful sedation side-effects at high doses but not at low doses), etizolam, Librax (very old, works very fast, very potent but can cause aggressiveness and impulsivity), medazepam, Ox-Pam (not very potent), pinazepam (few to no cognitive side-effects), prazepam (fewer cognitive side-effects but more than pinazepam) and premazepam (significant cognitive side-effects at first but with repeated exposures, they reduce a fair amount).
Remember all of them have some sedation effects as it's part of their way of treating anxiety.

The issue with benzodiazepines is they are addictive so if you're on them, it's not for a long time, usually maximum of 1-2 months. Azapirones on the other hand are less likely to be addictive so they can be used for long-term use. If the symptoms are severe and aren't being well-controlled, then you may be given benzodiazepines and the exact medications may be geared toward heavy sedation (i.e. not the ones I listed as I assume you're relatively stable). Such ones would be temazepam (used in the US Air Force to help pilots sleep when they cannot do so otherwise), Rohypnol and Erimin (knocks you out in around 15 minutes).

* = a few benzodiazepines, such as clonazepam can have cognitive side-effects lasting up to half a year. Most of them will not but this one has a well-documented history of that.
** = certain types can be very potent to sedate aggressive psychiatric patients who won't comply.