Assets: $22,000 cash, plus $24,000 spare cash coming in each year.
Liabilities: student loan of $34,000 @4.5%, negative equity in tenanted house of $26,000, total $60,000.
You could pay off the student loan within the year while still ending up with an emergency fund of $10,000.
You say that the rental house is not cashflowing and is unlikely to do so, but that we are to assume the cashflow is roughly breaking even. I agree you want to keep good tenants, but if you can negotiate a cost of living/inflation increase into the rent for the new lease, that could help the cashflow. But the last thing you want is a void, as this would wipe out the benefit of any increase and send the cashflow negative, so you need to judge carefully your tenant's receptiveness to a proposed increase and/or the possibility of getting good new tenants in quickly.
Will the house increase in value within any timescale you are interested in? If there is potential for a capital return, then your current break-even cash flow is a no-cost way (other than your time and effort managing the property) of keeping the potential for that capital increase. If there are no potential increases in value within your timescales, then I would suggest keeping the house until you have whatever cash you need to bring to the closing (so you don't have to borrow)and then sell, as that would leave you free to start investing your $24,000 a year to its maximum potential.