Appendix P, P2 method is based on two articles by Billimoria and Hagstrom/ Billimoria and Tam.
This appendix is intended to be used for tanks larger than 36 m (120 ft) in diameter, and only when specified by the Purchaser for tanks 36 m (120 ft) in diameter and smaller. One reason is due to the fact the equations the authors used for calculating tank shell deflection and rotations assume that the bottom to shell joint behaves as a hinged connections.
You may compare this assumption with the "modern" assumption as in API 650, 5.6.5 Calculation of Thickness by Elastic Analysis
"For tanks where L/H is greater than 1000/6 (2 in US Customary units), the selection of shell thicknesses shall be based on an elastic analysis that shows the calculated circumferential shell stresses to be below the allowable stresses given in Tables 5-2a and 5-2b. The boundary conditions for the analysis shall assume a fully plastic moment caused by yielding of the plate beneath the shell and zero radial growth."
Now you have a "small"” tank out of API 650 scope and out- anyway- of scope of Appendix P2.
You are looking for an analytical method able describe nozzle deflections/rotations and allowable loads.
Such analytical approach would be developed based on a method able to describe analytically the bottom to shell joint behavior.
I don’t know such method.