Generally CAESAR results become suspicious when you have two supports put so close together - due to modelling technique more so than CAESAR itself.

Have you done any of the following:

1) Considered thermal expansion of the box header from the bottom of the box header to the nozzle elevation?

2) Considered the flexibility of the nozzle/box header connection? (NozzlePro offers this.)

3) Calculated stresses outside of API-661? (NozzlePro offers this.)

In addition, I'm not a fan of flange supports as typically stress analysts aren't prompted to do any additional work to qualify them and what they do to the bolts, and there's significant overhead to achieve this on a per-flange per-flange rating per-size per-flange support detail level.