Lee,
You should be able to use the design for the 12" on the 8" & 10". The material lists 5/8" eye-bolt and plate. With this size, you will still have nearly 0.25" on both edges of the flange for a fillet weld (8" - 150#). The davit will be a little over designed, but shouldn't present a problem. I have not worked with PD5500, Specification for Unfired fusion welded pressure vessels, so I cannot be sure how it addresses structural members. Under ASME VIII, D1, you should consider the davit a nonpressure attachment. Non Mandatory Appendix G, Suggested Good Practice Regarding Pipe Reactions and Design of Supports and Attachments may be useful.
The third party inspection will typically review the construction drawings and make sure that the attachments have been built as designed. They will visually inspect the attachments welds and may PT or MT them as well. Obviously, the design materials of the attachments will need to be compatible with the vessel and the welding will need to be covered by an approved welding procedure.
Best of luck,
John