Presta valve in a Schrader rim hole: How to use / do I need a rim hole reducer?
With the Mavic adapters, the lip is supposed to go on the outside. They're not intended for use with single wall rims, hence the problem you're having.

On a single wall rim like yours with the relatively deep, narrow channel in the rim well between the reinforcing sections, none of the reducer grommets available are going to work very well. The other option are the aluminum ones, which are usually superior, but they install on the inside and here they wouldn't work.

Those Presta nuts that sink into a Schrader hole are bad news. They do nothing to prevent the core problem of Presta tubes in Schrader holes, which is stress around the valve from not being supported by the rim eventually causing the tube to rupture. Maybe on a single wall rim this is less of an issue, but I still don't like it.

Just use Schrader tubes. 700x23-25 / 27x1 SV tubes are perfectly common.