Nobody has asked the question that decides this, so let me: WHY did the HAP go from 2,000 to 500?
I run a few hundred voucher doors and I have never once seen an authority cut a HAP by fifteen hundred dollars arbitrarily. The housing assistance payment is the lesser of the payment standard or the gross rent, minus the family's total tenant payment, which is roughly thirty percent of adjusted monthly income. So a swing that size means one of three specific things happened, and which one it is changes your entire decision.
ONE - THE HOUSEHOLD'S INCOME WENT UP. Someone got a job, or a working adult joined the household, or income that was previously unverified got verified at recertification. The tenant portion rises and the HAP falls by the same amount. Note what this means: the tenant is not poorer, she is richer. She may genuinely be able to pay. She may also have had no idea the increase was coming until the notice arrived.
TWO - THE HOUSEHOLD SHRANK. People moved out, the family now qualifies for a smaller bedroom size, and the payment standard that applies to them dropped with it. This one matters most, because it means the family is over-housed in your unit and the fit problem is structural rather than behavioral. That tenancy is probably ending regardless of what you decide.
THREE - A RENT REASONABLENESS OR PAYMENT STANDARD REDETERMINATION. Less common at this magnitude, but worth ruling out.
You are entitled to the owner copy of the rent change notice showing contract rent, HAP portion and tenant portion. Call the authority, ask for it in writing, and ask which of the above drove it. That is a phone call and an email. Right now you are contemplating a 350,000 dollar decision without the one piece of information that determines whether this is a tenant problem, a fit problem, or nothing at all.
THE PART THAT IS NOT ABOUT THE TENANT
Separately, and I say this plainly because I think it is the real answer: the voucher change did not break this property. It revealed something that was already there.
2,500 rent against a 2,000 mortgage is 500 dollars a month before taxes, insurance, maintenance, vacancy and capital. In Florida, insurance alone can take most of that. That was true last year at full HAP. What you had was a property that looked fine because the money arrived on the first without fail, and reliable income is very good at hiding a thin spread.
So you have two questions, not one, and you are currently answering them as if they were the same question. Question one is what to do about this tenancy. Question two is whether a 2,500 rent against 2,000 of debt service is a business you want. Diagnose the first before you decide it.
ONE THING IN YOUR FAVOR THAT YOU ALREADY SPOTTED
You are right about the rate, and I would weight it more heavily than you are. A 3.5 percent note is the single most valuable thing in this deal and it is not replaceable. Trading it for today's rate on a similar basis is exactly the problem you identified yourself. Trust that instinct. The tax side of a 1031, including depreciation recapture and what paying the loan off does and does not change about your gain, is a question for a CPA rather than a forum, and I refuse those on sight.
AND ONE THING I HAVE TO PUSH BACK ON
The tenants usually section 8 and trash the house. With a few hundred voucher doors I will tell you straight that damage tracks screening and management, not the voucher. The voucher describes how the rent arrives, not who the person is. If anything the program gives you something market-rate landlords never get for free: a third party inspects your unit on a schedule, which is an annual condition audit somebody else pays for.
The lever is screening, and you can screen a voucher holder exactly as hard as anyone else. Call the prior landlord yourself rather than taking a reference letter. Ask the one question that gets an honest answer: would you rent to them again.