Tire size also enters into the equation. But 3.37's are a pretty high ratio. A 350 is not an overdrive tranny but with 3.37's and assuming you have a decent size tire, you could be in trouble with a 2,800 rpm stall converter. My "dream wheel" as we used to call them, is at home. It is a circular calculator that you can set your engine final drive ratio, tire size, and rpm and it would tell you how fast you will be going. Isky used to sell them. Maybe they still do. If you are good at math you can figure it out by yourself. As a very, very rough guess....and I could be off...I am thinking that you will have to be going at least 60 before your converter gets out of the stall speed range. And not knowing your tire size....for sure that is just a guess.
On my '33 Ford, I am running a 3.90 rear but with a 70% TH-700 overdrive, which would be the same as a 2.73 rear. But I also have really big tires....32" which is the same as running a higher ratio (lower numerically) rear. As I said before, with that combination I am turning 2,100 rpm at 70 mph. With smaller tires, and a lower gear ratio your engine will be turning a lot faster....good for a high stall converter....bad for fuel economy.
If you do go with a higher stall converter, just make sure you have a big trans cooler (preferably with a fan as suggested earlier) along with a trans temp gauge so you know if you are getting too hot and can pull over and let it cool down.
Special note to Chris: Who you know is good. But what you know also helps a lot too.
I just remembered that GM made a lock-up convernter for 350's. Whether B&M, or anyone else for that matter, makes a high stall version of this converter, I don't know. You might call B&M and ask them. A lockup converter is frankly the way to go if you can.
When I first built my current street rod, I burnt the tranny up in the first year because 99% of my driving was in the stall speed range of the converter. So when I had the trans rebuilt, I had B&M make me a stall speed lockup converter. B&M also has a device that you can use to control the point where the converter locks up. I have mine set to lock up at 40 mph. That was nine years ago and I haven't had a problem since.