Just a few comments -
1. The smallest tires/wheel you found may not be adequate to support the wheel loading when the unit is driven empty. Approximately 65 -70% of the GVW empty is on the steering tires. This is one reason why steering tires wear out at twice the rate as the front tires. The tires & wheels need to be sized accordingly. You will find that tire sizes front & rear will vary from one manufacturer to the other for units with the same basic capacity rating. This is primarily due to the axle ratings difference which will vary due to various factors such as wheel base, front over hang, mast weight, etc, etc. In other words - not all forklifts are alike.
2. Likewise, the driving tires are under most load when the truck has a load on the forks. Even though you state that you handle loads under 2k "most" of the time. This statement also implies that "occassionly" loads greater than 2K are also handle. The front tires need to sized to the max weight the unit is designed to handle. This kinda' like saying you go bass fishing using 4 lb. test line becaus most of the time you catch 1-2 lb fish. You know what happens when the occasional 10 lb lunker hits. Guess I wouldn't want to be the one of 2 authorized people to operate the lift (or other folks working/standing nearby) when that "lunker" hits.