Some time earlier this year I inquired of the MRA/MGTOW crowd what they wanted in order to be willing to play the marriage and child rearing game once more.
From the various comments, I believe that a reasonable accomodation could be reached between this group and the social conservatives at large. Here's what I suggest:
Create a new available class of marriage. This will have a lot of similarities to the 'Covenant Marriage' that is available in several states in the US. The specifics would include:
1. Much more difficult divorce--basically only the 3 A's (adultery, abuse, abandonment). Nothing like no-fault divorce would be permitted. MRA/MGTOW know very well that most divorce is initiated by women, but this could be sold pretty easily I suspect to social conservatives and would-be white knights as making it more difficult to dump a faithful wife for a newer model.
2. In the event of a divorce, the children will default to the full custody of the father. This could be sold based on statistics (children with only a father do better on most metrics than children with only a mother) and as nipping the whole 'deadbeat Dad' meme in the bud. MRA/MGTOW will of course realize that this puts some shackles on the rationalization hamster by increasing the perceived cost of a divorce to the female partner.
3. Prenuptial agreement would be mandatory. In addition, filing for divorce in a state without this flavor of marriage recognized in statute would trigger a provision in the prenup making is VASTLY more unfavorable to the one so filing. Basically, if you try to get around Provision 1 by divorcing in a state that doesn't recognize this flavor of marriage, the prenup will punish you severely. The arbitrating agency for the prenup should also probably be required to be defined at time of signing, be it a secular or religious agency.
So would this arrangement tempt you sufficiently? One could probably get a reasonable facsimile of this via contract + covenant marriage in the states that have covenant marriage presently, and getting something like this codified into law in at least one state is probably not an unachievable goal.