OK, that oriface sounds like it's in the ball park.
I think it's already been said but your flame is too rich, IAW too much gas for the amount of air being pulled into the burner. As such you're trying to decrease the fuel/air ratio. So for the same regulated pressure you need a smaller oriface or for the same oriface a higher pressure. This happens because the air gets pulled into the burner by the venturi effect, the higher the velocity of the gas coming out of the oriface the more air it will pull in. You can get a higher gas velocity with a smaller oriface or higher pressure.
I think your next step is to determine what burner element you have, whether it's a high or low pressure burner, and what regulator you have. Then see if it's a combination that is supposed to work well together. Based on your comment of "plugging 1/2 the holes in the burner", I'm going to guess you have a lower pressure burner because you can actually plug the holes. As such, my best guess is that you may have a regulator mismatch. You can usually figure out what pressure your regulator is by looking at the markings on it or by matching it up with one you can find online. Adjustable regulators with turkey fryers, (i.e. have the adjustment knob on top of the regulator) usually max out at 10 PSI. While 20, 30, and 40 PSI regulators are usually acutually fixed pressure regulators (almost always painted red BTW) with a needle valve somewhere down stream to adjust the output gas flow resulting pressure.
On my brew rig I have a 2 BG-10 high pressure burners, 2 #57 oriface (just a little bigger than your #60), and a 30 PSI regulator with 2 needle valves off a tee fitting that drives 2 of these burners. This all burns cleanly with a bright blue flame. I can get some orange in the flame by choking the air vent down to the smallest setting, but nothing that will create a lot of soot on a pot. This is burner:
http://www.bayouclassicdepot.com/bg10_cast_iron_burner.htm
If you have the burner in the link below with more than a 10 PSI regulator then you may have a problem. See the comment on the burner page.
http://www.bayouclassicdepot.com/bg12_cast_iron_burner.htm
If you have a banjo burner, like in the link below, then your only problem would be having a big enough regulator.
http://www.bayouclassicdepot.com/bg14_cast_iron_burner.htm
BTW, if you got your turkey fryer on special or on sale at Walmart there's a good chance it may have been a return or open box that someone else has already had a chance to mess with or swap parts with. If that's the case who knows what you really wound up with.
Good luck figuring what you've got. Post a pic or two here and one of us may be able to help you figure it out further.