I would hazard a guess that a successful one would work to avert or minimise the creation of nationwide, bourgeois political forces. This would mean addressing the issues that IOTL fuelled the creation of these forces, but doing so in ways that circumvent them.
While better ideas in this regard are certain to be possible, I think a decent shot at this would some kind of semi-democratic/meritocratic parliament, with one house filled by commoners via sortition ("selection by lottery"), not election as we are used to in modern liberal democracies. Elections mean political parties, hence organisations with long-term leaders that can rally supporters and start issuing demands to the King, and it means election campaigns, which guarantees that debates about how the country should be run and who should run it dominate the social conversation. In contrast, if a lottery picks out a random cross-section of society (or at least the part of society considered suitable for the role) and puts them in the role of representing the people to the monarch for a year or two, then the people selected will not have much incentive to empower a house that they know they will leave before long, they won't have a party or an electorate to be loyal to (I can imagine some kind of council of judges to check against corruption or deliberatively harming behaviour of the members at the end of their terms to minimise malpractice), there would be an avoidance of polarisation of parliament into staunch monarchists and committed republicans, and the people might come to the mind that whatever issues are worth addressing is being done so by the parliament so it's not that worth worrying about kingdom-wide politics unless they happen to be selected themselves.
The upper house might have some representation of the First and Second Estates, but its main body would be life-appointees of the monarch, perhaps about 150 seats in size. If the purpose of the lower house is to keep the government in touch with the needs of the people, the upper house's purpose is to give the kingdom's government an institutional memory and a stable element that can minimise the impact of inexperienced and incompetent monarchs. As the upper house would contain members of a wide diversity of ages, and the monarch would typically wish to maximise their influence by appointing the fairly young, it would be expected for the upper house to change in its composition by only a few members in any year. Ministry positions would be picked by a combination of monarchial appointments as votes by the upper house - let's say the Foreign Ministry is run by a college of seven, with the monarch appointing four positions and the house three, or perhaps the other way around in certain conditions (like the monarch needs special concessions like new taxes for their projects, or it is the first few years of their reign and so need experience in government before being trusted with the dominant role in appointments).
Finally, a continuation or a strengthening of the localism of medieval government, which a large amount of leeway given to large urban areas. It's for the monarch to be the guy ready to swoop in and deal with corrupt city elders than to be the done levying taxes and leaving bread scarce. I think a pillar of the monarch's rule would be the yeomanry who would supply the bulk of the wealth and bodies for the monarchs core institutions for keeping social order; the professional army, the intelligence service, and the granaries. It's important for the monarch to not let the city and country unite in common cause: that would actually be a good reason for the king to allow some amount of social liberalism in the towns, to alienate the two places from each other.