I used to own a Mokita. Youre doing the right thing turfing the turbo-frother its a little brutal at best. All it creates is very coarse dishwasher soap. :-/
What you said seems a bit odd. I used to be easily able to froth enough milk for two lattes with just the wand using a 600ml jug. Youre not pushing too deep or over-stretching your milk are you? All I did was stretch until about 37-38c. Then just push the wand a little deeper until 65c.
In other words start with your tip just touching the surface of the milk. You should be hearing psssshht, pssssht type of noise be careful not to pull the wand from the surface otherwise youll end up with large bubbles that dont break up. Once you hit 37-38c (you do have a milk thermometer dont you?) drop the tip further into the surface of the milk. Once you hit about 65c or so close the steam valve. Dont pull the tip from the milk until you do this.
Then when youre cooling your boiler whack the jug a couple of times on the bench to break up some of the remaining large bubbles then swirl your pitcher on the counter creating a whirlpool of sorts to smooth out the milk.
If youre new to all of this which I presume you are I cant understate the importance of a good milk thermometer (about $10). Makes life far easier and avoids a lot of mistaken temperatures. You should be able to steam enough milk for two cappas or lattes on a Mokita in about a minute or so.
You can make pretty acceptable microfoam with a Mokita like all machines it just takes a lilttle practice. :)