In my opinion, you are wasting your money if you don't change out the expansion valve and flush or change the evaporator. It's not a question of your problem being the expansion valve, it's not. The problem is that your whole system is contaminated by debris from the failed compressor. I don't think that you can effectively flush out the evaporator with the expansion valve in place. Just for the lines, you'll need professional help to flush them. The problem is that once flushed, you have to completely get rid of the flush chemicals too. This is usually done with nitrogen.
Anyway, if you don't get all the compressor particles and flush out, the new compressor won't live very long at all. (Of course, if your $188 compressor is anything like the one that I tried, it will only go a few months anyway.)
I guess that your low dollar option here is to just pop a new dryer and the cheap compressor in and see how long it takes the particles to destroy it.