I figured I would just point out two significant points in the Bible. Acts 10:43-48 clearly illustrates that one can have the Holy Spirit before baptism. The passage also says "whoever believes in shall have remmission of sins." Once you have the Holy Spirit in your life you are saved. Also, you mentioned when Paul was saved. Well, Acts 9:17-18 show that Paul was filled with the Holy Spirit before he was baptized. That account of Paul's salvation comes before Acts 22. I don't think you can get around this fact.
It has been pointed out before that people have received miraculous gifts of the Spirit without being saved. See "Is the Spirit only given to the obedient?" for details.
"And Ananias went his way and entered the house; and laying his hands on him he said, "Brother Saul, the Lord Jesus, who appeared to you on the road as you came, has sent me that you may receive your sight and be filled with the Holy Spirit." Immediately there fell from his eyes something like scales, and he received his sight at once; and he arose and was baptized" (Acts 9:17-18).
The order of events was 1) Saul received his sight, 2) Saul was filled with the Holy Spirit, and 3) Saul was baptized. You claim that at point 2 Saul was saved, but you offered no proof. This passage does not state precisely when Saul was saved from his sins. In retelling the events Paul recalled Ananias stating, "And now why are you waiting? Arise and be baptized, and wash away your sins, calling on the name of the Lord" (Acts 22:16). If Paul was saved when he was filled with the Holy Spirit, then he would have had no sins to wash away in baptism. Since he still had sins prior to his baptism, we must conclude that being filled with the Holy Spirit, in and of itself, is not the means to be saved from sin.
The case of the Holy Spirit coming upon Cornelius was dealt with in detain in "Cornelius Received the Holy Spirit." The fact that belief is required for the remission of sins (Acts 10:43) doesn't imply that it is belief exclusively. In fact Peter had earlier stated, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit" (Acts 2:38). Here both repentance and baptism are also listed as requirements for the remission of sins. The truth is in the sum, not the parts. These two verses tell us it takes all three: belief, repentance, and baptism to be saved. Yet this isn't an exclusive list either. Other verses tell us that other things are necessary as well.