@Aaron Miller, since you are okay with paying that rate long-term, a cash-out is probably better for you. That way, you lock in the rate without having to worry about the rate going up and up. However, ask the brokers you are shopping with to give you a side-by-side comparison.
I recommend using both a broker and shopping around. Each broker is priced differently so I would shop around with 3-4 different ones.
To properly shop, make sure you get rate quotes on the same day as rates change daily. Then, you will want to ensure you give each lender the exact same information. Finally, you want to ask for “par rate”. That means you will not pay any points to buy down the rate.
You do not need to fill out an entire application to get a rate quote. The lender only needs to ask you a few questions. You have 45 days from your initial credit pull to shop around with as many lenders as you would like without it hurting your credit.
Hope this helps! Let me know if I can be of any assistance or if you want to shop with me as one of the brokers.