I'll at least leave my message for you here.
First, just get a CRT. CRT's have no lag, unlike an LCD. You can find a good CRT tv in a thrift store or goodwill/salvation army for 10 bucks or less
Second, you seem to know how to do a lot of the basic tech (waveshining and whatnot) but just practice using Falco's laser too. SHL and all. Grind techskill when you aren't playing in tournament (and do this on a CRT man)
Other than that, you can learn alot about Falco's combo game here on the boards and I think the people in the video thread can elaborate for you, since you are practicing on a CPU, I can't really tell you what the best option is, because that would be redundant.
Good luck training!