I'd argue that you could use the proposed method to approximate stresses in smooth forged crosses conservatively, but would be nervous about using this on an actual fabricated cross made with 4 pipes cut at 90° angles without a safety factor.

Instead of marrying the results to ID, I would use a static value, such as subtract 0.01"-0.05" from the radius. This is similar to attaching trunnions to elbow extradoses in FEBend. If you push it as far as the software permits, it will often diverge to unrealistic numbers. Make it too small, though, and stresses will be under-reported.