You can't get dehumidification if system is .not running in borderline situation like yours.

Your description suggests that temperature setting is satisfied but your home is getting infiltration to make home muggy/clammy feeling. The only way is to pull thermostat setting down to try to remove humidity through AC cooling.

Newer systems couples with var speed furnace or air handler can be set with dehumidify on demand where even when thermostat is satisfied, an independent humidity setting will force AC cooling to come on at a low blower speed to take humidity out of home.

You might want to check the blower speed setting on your air handler or furnace. Should be no more than 400 CFMs. Definitely AC cooling should be set to auto not fan on blower setting.

IMO

Get a couple of hygrometers and measure the humidity.

1. measure humidity so you know what it is. it should feel comfortable if below roughly 50%

2. slow down the CFM so that the A/C runs longer

3. if it is oversized, you will have issues with humidity as A/C will cool down home so quickly it has no time to dehumidify.

My unit is new: Lennox with icomfort xstat and it has a mode that dehumidifies by slowing down the fan whenever humidity is above the setpoint (i can set that point on the xstat).

If your system has a TXV metering device to feed refrigerant into the evaporator you could slow the blower to around 325-CFM per ton of cooling & the TXV will throttle the refrigerant down which lowers the Btuh of the system for longer runtimes & a colder coil with a longer time for air within the fins of the colder coil.

You can buy low cost SWING programmable thermostats whereby you can set the runtime differential temperature.

For dehumidification you do not want the A/C to cycle more than twice within an hour.15-mins on; 15mins of twice.

Less than twice an hour is even better.

Here is a link that might be useful: Latent Heat Removal - Equipment Sizing

The humidity is 57 to 58......according to my hygrometer. Is this good? What is considered a comfortable humidity level during the warm and humid summer months?

50 RH and below...

like tiger said: under 50%