Can you increase the speed of an ECM AC blower?
When you asked to increase the blower, what you are really asking to do is increase the fan speed (amount of air), right? You could ask the the tech to check/verify that you are getting 1600 CFM (cubic feet per minute) and if you truly are, and if that's not enough, ask them if it is possible to increase it (it might be adjustable). But I am thinking that may not really be the issue. 

Your real problem is that it's not cooling the house. I'm not sure if this issue is truly the result of a weak blower (insufficient CFM); it's very possible, but honestly, a 1.5 ton unit is pretty small. For a 1,000 square foot house, I might recommend at least one 3 ton unit or preferentially, two 2 ton units, depending on your lattitude (summer temperature). Below is a map and chart. I would generally recommend double the what they recommend on the chart below, because you will only use what you need. 

In case you didn't know, having more (AC tonnage) doesn't mean that you will use more. If you set the thermostat to say 70 °F, then the AC will turn off when the house is at 70 °F. If you have fifteen 3 ton units, you will use the same amount of energy to cool the house to 70 °F as one 2 ton unit (give or take maybe 5% energy).



Map source:http://www.acdirect.com/ac-package-unit-learning-center-ac-sizing-calculator

Edit based on comment that the AC is actually a dehumidifier:

Dehumidifier? Well, that's a key piece of information. The old unit may not have been well designed as a dehumidifier; if the newer unit has been set up to be more like an actual dehumidifier then that would explain the question. The older unit was probably designed (more) for cooling. The newer unit might be a more for dehumidifying.

The difference between an air conditioner and a dehumidifier is that the air in a dehumidifier first passes through the cooling coil and then back through the heating coil (basically, there will be little change in room temp) and then back into the room as dry air. In fact, the temperature might be higher.

Unfortunately, this means that the answer is to install an actual air conditioner or re-engineer the dehumidifier to make it an air conditioner.

Edit2 Okay it's not a dehumidifier. It's a regular AC and you have a separate dehumidifier. Regular AC units have protective coatings to help prevent condensation on the evaporating/cooling coil. That protective coating usually doesn't last forever which is why older AC units often collect water. Typically, you don't want the AC to collect water (that causes rust and mold issues). For a regular AC unit, having the blower on high is okay. Lower speeds (lower CFM) may cause condensation to occur (depending on all the bells and whistles). 

The dehumidifier is where you do want condensation- to remove moisture. Cooling the air should help your dehumidifier to operate, because as the temperature is lowered, the relative humidity will increase. When measuring the relative humidity, the temperature is a/the factor. For example, say that you have 44% humidity at 70 °F; it has about 0.26 grams of water/vapor per cubic foot. At 50 °F the relative humidity of 0.26 grams of vapor per cubic foot would be about 92%. A dehumidifier should be able to operate more efficiently at 92% RH than 44% RH... so that's why an AC unit can help a dehumidifier. 

I suspect that when you measured the RH in the basement it was higher than you expected (maybe about the same as the RH outside), but if the temperature was lower in the basement (than outside), then having the same RH means that you actually have less water vapor in the basement, where it's cooler.

To recap: The service technician might be able to increase (or decrease) the blower speed, but that would probably lower the AC's cooling efficiency. Your new AC unit is not collecting water (yet) because the anticondensation coating hasn't been compromised (yet); and that's a good thing. A 1.5 ton AC unit may not be large enough to cool the basement. Cooling the basement should help the dehumidifier. And remember, the relative humidity is based on the temperature.