My hypothetical assumes that the team was writing 95% accessible software already. The last 2 weeks are for the final push.
Of course, if this is a truly all-or-nothing thing where you need to do it 100% perfectly to incur no extra cost, then that strengthens my argument for the compatibility layer, it doesn't diminish it. Very few non-specialists can get something 100% right on the first shot.
Definitely, the most expensive way to add accessibility, is to retrofit it.