For my 2 Eurosworth - yes, I would have been more forceful in the RHS about the speed during entry. Was it briefed? If so did you challenge it?
A 'smart' way to solve the procedure problem is to get yourself onto the 249 radial BEFORE the VOR and go straight outbound. Whether or not it would pass an IRT I know not, but it is SAFE and WORKS.
Edited to add: - and AMZINGLY easy with EFIS
