It is NOT an "appeal" to God for a good conscience but is actually having received a good conscience by the Holy Spirit through Christ.
Why would two baptisms be necessary? The verse says "not the putting away of the of filth of the flesh" - putting away the filth of the flesh is water baptism - and is only symbolic of the cleansing and removal of spiritual sin, but not the actual removal of it As the verse says, that will not save us, instead, the baptism that saves was brought by the resurrection of Jesus Christ. The 'good conscience " is given through being spiritually baptized (cleansed) by the resurrection of Jesus Christ, through the Holy Spirit, by which, we are truly cleansed of sin spiritually with nothing further needed. Being washed in water is meaningless for the removal of sin and was intended only as demonstration. The filth of sin exists upon our soul in the spiritual realm, not upon our skin in the physical realm - doing something in the physical realm has no significance whatsoever in the spiritual realm - to be significant, it has to actually occur in the spiritual realm, however, it is not possible for man to make that happen.
Again, you just simply cannot accept that Christ is the Saviour in all ways and that man is not. I believe it is all by Christ and nothing by man, So, there is just too large a divide between us to make discussion meaningful.