The 1/2-ton kit from Patrick's won't help you as you already recognize.
You have two basic options as I see it.
1) You can change the gears in your current rear, going to the standard 3/4-ton set which is 4.57 instead of your current 5.14, or searching out the hard to find 4.11 from a later truck using the Eaton rear.
The 4.11 (4.10?) gear set is hard to find by all accounts. You may happen on one easily, or may never find one. I know a guy who was given one for carrying it away. Other guys have searched high and low and not found one anywhere.
There are rummors of a gear set more like 3.70 but no one has ever convinced me they have found an Eaton gear set in that range. I think they have confused it with a Dana rear that was used under early 70's 3/4- and 1-ton trucks.
2) You can change the entire rear axle. This opens up lots of options and means dealing with some questions.
First the options... They are many. The Dana 70 series of axles seem a good choice as do the GM 14-bolt rears. There may be others. When I changed mine I chose a GM 14-bolt mostly because I had one that already had the right spring pads on it and a gear ratio (3.54) that I liked.
The GM 14-bolt comes in two widths if I remember correctly and you'd want to shop for the one that best fits your needs. There is a semi-float six lug version of the GM 14-bolt and you don't want one of those.
I have a couple of Dana 70 HD axles on hand and one is from a dually pickup and far too wide to go neatly under my '55 1st 1-ton. Both my Dana's have 4.11 gears though I don't believe that would be difficult to change.
The Dana was used under more different trucks than the GM axle. You might find it under a Ford or Dodge and will definitely want to have thought through width and brake issues before going shopping for one. Do you have a pickup bed with fenders or a flat bed? If a pickup bed you really do need to be more careful to get the right width axle.
Some things you need to think about before axle shopping are gear ratio (easier to buy the one you want than change), WMS to WMS width (how wide do you want to be?), and brake type because the axles are available with either disk or drum brakes.
I mentioned the 14-bolt I put under my truck. I'm running a Cadillac 500 with a TH 400 and do not expect to have any trouble moving a load. I got the axle from under a '50-ish 1-ton with a tired 216 and an SM420.
The guy I bought it from was selling the truck because it was not capable of hauling a load and was difficult to move even empty. Now this was a tired motor, but the issue remains you need to have carefully considered how you are going to use the truck and make sure you've matched the gear ratio you choose to your needs and available power.
If this truck runs around empty, but is powered by a tired 228, your best bet may be to look for that ellusive 4.11 gear set. You'll have a drivable truck that will run down the highway, but not give up so much torque multiplication that it requires a granny gear start. I don't know how badly that 216 ran, I never tried to start it.
So that should give you a start and someone will come along with something I missed or a different opinion...