Part-time Realtor and small-time landlord here.
Generally I agree with MMM that
if you wouldn't buy it, you should probably sell it. I am, however, currently tied up in a very similar situation, though my numbers aren't quite as bad, and I'm holding for largely the same reasons - transactional costs would mean a loss today, but a couple of years' hold time could help me avoid bringing cash to the table.
The biggest caveate to keep in mind, IMHO: every year of rental depreciation reduces your cost basis by a few percent, so you'll eventually show a large capital gain subject to depreciation recapture tax. If you lived in it for at least 2 years within the 5 preceding the sale, you get some preferential treatment, and active military service can extend the 5-year clock, but you should get acquainted with the particulars sooner rather than later! I keep a constant eye on the clock with mine.
Your analysis is very optimistic on costs. Are you really spending $0 on repairs, cleaning, maintenance, etc? No pest control? Nothing else? Are you doing 100% of that work yourself, counting $0 value for your time? I'm nominally clearing $250/mo after HOA (I manage it myself, though the next turnover will be the end of that) but even minor maintenance can wipe that out in a hurry. In your case it could turn your miniscule cap rate (after equity build) into a strongly negative one.
I considered dumping some cash at the principal and reamortizing to force it cash-flow positive, but from what I read it's not possible to reamortize a VA loan and I'd have to figure out some other solution (take out a different mortgage?)
Unless the negative cash flow is hurting you, and it sounds like it's not, then don't factor it in. Return rates should be the primary determinant.
You'd be earning a guaranteed 4.25% return (ish) on that paydown. It's your call. Personally, I'm leaving my albatross alone, maximizing stock investments (historical average 7% after inflation) and more real estate (multifamilies with leveraged returns of 20% or more). This means more total NW increase over time, and I can draw on those returns later if I have to sell and it's still underwater.
If you do decide the cash flow is an issue, and you want to reduce the payment, you could look into an IRRRL (inline rate reduction refinance loan). It's a low-cost refi for a VA loan that you can do even if the home is now a rental. I just did one a few months ago. Since this is your bonus entitlement, I'm not 100% sure if all the same rules apply, but a good mortgage broker or loan officer can tell you.
If you decide to sell without an agent, find a good real estate attorney and have them do the contract for the sale. Also, review that commission clause carefully and see if it's negotiable at all, or has a timeout. Is the percentage specified? All commissions are negotiable unless/until agreed upon by the principals involved.
Also, just a side note here, for if/when you have to analyze potential rentals in the future:
still a poor cap rate, since we put very little down
If the property was a good rental, lower equity would
increase the cap rate because you'd be netting a higher return on your investment than the APR on your associated debt ("spread"). Most multifamilies earn enough rent to finance them 100% and still pay the mortgages after all costs, and that's what rental investors look for.