Three British treaty replacements: battleships or battlecruisers?

If Britain freed enough treaty tonnage for three new capital ships, would all three resemble Nelson and Rodney?

There is disagreement. One proposal favors three fast battlecruisers with six 16-inch guns each; the counterargument expects two Nelson-type battleships and leaves the third ship open to a different design.

The additional treaty tonnage produces two competing plans. One proposal calls for three battlecruisers with six 16-inch guns in three twin turrets, preserving speed and protection. These ships could alternate with Hood, Renown, and Repulse as groups entered refit. The counterargument rejects that rotation scheme as too modern for contemporary policy and expects two Nelson-type battleships to remain in the program. Under that interpretation, the third ship could explore a faster six-gun or nine-gun design. Political attachment to the battle line, particularly Churchill's, is given as an obstacle to choosing three battlecruisers.