2001 Honda Civic A/C troubles

So prior to this summer my ac wasnt working for about 3 years. I had it looked at and the compressor was dead. This year I had a tech replace the compressor. He said there was something else he was gonna replace that usually gets done with the compressor though I dont remember what it was. It worked ok, but it seemed to be short-cycling on the highway and putting massive strain on the engine (it ended up killing my already declining tranny and the tech who replaced the tranny mentioned the term short cycling to me). Anyways I ended up having the whole system flushed and filled cause the output was only 70% and I believe the tech who replaced the compressor only drained and filled it, didnt flush out the 3 yr old fluid.

so where I am at now is that the short cycling is drastically improved, but when I turn on the ac after the car has been sitting a long time (more so in the heat) you can hear the compressor come on out the window, but the cold air doesnt blow right away. Sometimes it takes 10 - 20 minutes to get the cold air. I mean the cold air is really cold it just takes soooo long to get that point from when I turn the compressor on till the time it comes out the vents. What do you think I need to do to make the cold air blow almost instantly?