Let me please bring in some light;- the ASME SA-36 is a permitted material for use in ASME VIII Div 1, as it is listed in ASME II Table D. The ASTM A-36 material may be used under the ASME BPV code, provided is certified for compliance withe ASME SA-36 specification.
However, CCB1 called his equipment pressure vessel, despite the mentioned design pressure of +/- 6 psig (???). Remember, the minimum pressure to qualify the vessel as pressure vessel is 15 psig, anything less is not covered by the BPV code ASME. Did you read the applicable design code on the vessel nameplate?
I assume that the mentioned door is some sort of quick opening access cover and is not welded on the shell. I also assume that the mentioned code (ASME Section 7) is in fact Section VIII for the design of the pressure vessels, not the guidelines for the boiler care (it sounded a bit scary that the shell of a pressure vessel is designed by the Structural department under ASME section 7).
As such, you can use the SA-36 plate, provided is correctly designed for the mentioned design conditions.
cheers,
gr2vessels