At your income, I would guess that you will not be able to get a monthly payment low enough to stretch your loan out for longer than 10 years. However, even if you could, I would not recommend the loan forgiveness program for you.
I realize that $28k sounds like a lot of money, and it would be nice if you didn't have to pay it. However, the PSLF program lasts 10 years before you see any benefit. You and your wife have a high income, and you should be able to pay off this loan much, much quicker than 10 years. (One or two years should be your goal.) The quicker you pay it off, the less interest you will pay.
If you decide to pursue the PSLF program, you will be stuck in your current job for the next 10 years.
You didn't specify what your monthly payment is, or what the current length of the loan is, but let's look at a few scenarios.
Let's say that you were somehow able to get by with interest-only payments on the loan for the next 10 years. (I don't think this is possible.) In this scenario, you would be paying $140 per month, $1680 per year, or almost $17k over the next 10 years, and you will remain $28k in debt until you complete 10 years at your job, when you'll get the debt forgiven.
Let's say instead that you arrange a $200 per month payment. (At your income, I don't think you'll be able to obtain a monthly payment this low.) Without the PSLF, this would pay off the loan in 20 years. You would be paying $2400 per year, or $24k over the next 10 years, and at the end of the program you'd still have over $18k of principal that would need to be forgiven.
With both of these situations, it is true that you end the program with significant loan forgiveness. However, you are still paying a lot, and since most of it is interest, you still remain at a very high debt burden. If you need to leave your job for any reason, it will be a tremendously costly decision.
Instead, let's say that you decide to skip the PSLF program, and just pay it off as quickly as possible. If you pay $1250 per month, you'd have the loan completely paid off in 24 months, paying a total of under $29.8k, meaning that you will have paid less than $1800 in total interest.
Scenario 1: $140 per month, $17k total cost, 10-year commitment (not really possible)
Scenario 2: $200 per month, $24k total cost, 10-year commitment
Scenario 3: $1250 per month, $30k total cost, No commitment, 2-year payoff
The idea behind the PSLF program is to provide relief for people with a very high student loan debt and reward them for taking a low-paying public service job. You, however, have a great income, and can afford to pay it off early. If I were you, I would not want to make the 10-year commitment to a job just to save at most $6k (probably less).