I have been with a property management company for 2-3 years in Arizona and the property is being run continuously at a loss.

I recognize there are other ways I could invest this cash (including another property) but I am being mindful of levering myself out too much in the current environment where job losses are more common in my industry (tech).

Though at 1525/mth it is projected to cashflow a little less than 100/mth  -- the numbers do not include what I like to call reality numbers (vacancy loss, maintenance, capex reserves).

If I was to trade a $300k house for a $310k house that will cost me $10k and $347/month what amount should I ask for to make up for these losses?

Repairing to sell might recoup some costs, but given the market and your limited funds, selling “as-is” is likely the best option to minimize further losses.

Trying to cut my losses as the borrower got all her unsecured debts discharged through Chapter 7.

Let the tenant vacate, and you have one month to find a replacement before you incur any losses.

If they didn’t have replacement cost, what should they do to capture value and get a loss writeoff?

Focus on tax-saving strategies such as cost segregation studies and bonus depreciation to accelerate deductions.By qualifying as a Real Estate Professional (spending 750+ hours annually and materially participating), you can offset your wife’s S-Corp income with real estate losses, reducing your tax liability.

It's simply factual:  you violated the lease by smoking, stop it, remove the resulting odor and that a repeat action could result in eviction and loss of security deposit.