Could Britain trade gun calibre for a third treaty battleship?

Could Britain have accepted 15-inch guns in exchange for permission to build three new treaty ships instead of two 16-inch battleships?

Probably not, because the proposed 15-inch/50 would have been too close to a 16-inch weapon in practical power for other treaty powers to treat it as a meaningful concession.

A 15-inch label might appear to be a concession when other powers were adopting 16-inch guns. The 15-inch/50's penetration and hitting power would undermine that case because foreign negotiators would judge capability rather than diameter alone. Permission for a third ship would therefore be difficult to obtain. If Britain had secured three ships at the full 35,000-ton limit, the faster F3 concept was the likely beneficiary. The exchange connects weapons performance directly to the credibility of a naval-arms-control bargain.