MAP only exists in UCS-66, and is calculated per component in the hot and corroded condition. You cannot speak about MAP for a vessel.
However you can determine the MAP of each component, apply a product head correction to convert it to a pressure at the top of the vessel, and select the smallest of these values. This is the MAWP. The Code permits the design pressure (DP) to be used as the MAWP. If you order the exact design thickness material for even one component then MAWP will equal DP. MAWP will only be higher than DP when all the components are thicker than design. MAWP is used to calculate the UG-99(b) test pressure as you've discussed above.
The hydrotest is meant to be an overstress test to prove the vessel quality. That's what the 1.3 factor is trying to do. However for vessels with large corrosion allowance, the stress in the shell during a UG-99(b) test could be less than the actual stress will be in the future corroded condition! Thus the UG-99(c) test calculates the MAP of each component in the new and cold condition, multiplies by the 1.3 factor, and then corrects for the hydrostatic head to the top of the vessel. The smallest of these values is the calculated test pressure (CTP). There is no temperature correction (LSR) since the calculation is done in the cold condition. The CTP includes the 1.3 factor on each component, so 1.3 is not multiplied afterwards. This higher pressure assures that vessel is overstressed during hydrotest to prove it's quality.