If you are going to try to find a succession of valid Baptisms from Apostolic times to today, make sure they are valid baptisms. In other words, if you would not accept a man with that baptism into your Church membership, you can't accept him into your pedigree.
For most Baptists that would mean:
1. Baptism on profession of personal faith in Christ. It is not enough to be baptised because you have been through a course of instruction to prepare a person for baptism, there must be a confession of Christ as personal saviour.
2. Baptism with water. A symbolic rite involving tapping on the head with a copy of John's Gospel (which is what the Bogomils did) is therefore out of the question. Yes, there have been groups that have used 'Baptism' to describe a rite without water. We would not accept waterless baptism today, and if you would not today, you cannot accept it in the past.
3. Trinitarian Baptism. All Trinitarian groups would agree that a baptism that is not Trinitarian is not valid. Thus a Presbyterian might argue that Roman Catholic baptism is valid, but Unitarian baptism is not. So if a group can be shown to have been non-Trinitarian, then it cannot have had a valid baptism. Baptists hold not only to baptism on profession of faith, but also that it has to be the right faith!
4. Baptism by immersion. Practically all, if not all, Baptist Churches teach that immersion is the only valid form of baptism. If this is the case, then you cannot claim that a group that baptised by pouring or sprinkling, even if it was on a correct profession of faith, is in the succession of valid baptisms. If you don't accept it today, you cannot accept it in the past.
5. Denial of baptismal regeneration. Where baptism is seen as actually effecting the new birth, this contradicts Baptist teaching that baptism must follow a person's becoming a Christian. I am not altogether certain that all Baptists would reject a Cambellite baptism where it was understood that the baptism effected regeneration (and indeed there are a number of Baptist Churches that started out as Campbellite), but it certainly leads to some serious questions!
Now, it simply cannot be proved that every one of the groups in the claimed Baptist Succession was not flawed on one or more of these points. Many of the witnesses called upon by the Successionists are flawed at one or more of these points. I would therefore continue to say that Baptist Successionism is a figment no man can prove. It is an imitation of Rome, and if I may say so a far more shaky one. For Rome simply requires that one man laid hands on another, no matter what his doctrine or the ceremony in which the hands were laid on. But the Baptist Successionist must not only have a line of baptisms, but a line of true doctrine, and of the right mode and method of baptism!