The most common tools are the government's spending powers and the government's taxing powers.
Governments routinely pay people to do things deemed socially valuable, either as government employees (e.g. all of the Orthodox Priests in Greece) or through government grants (e.g. New Zealand's Wizard of Christchurch who was funded mostly with a government grant). Lots of academic and scientific and medical research and educational work gets funded this way. And some of the workers about whom complaints are frequently made about their social value not being adequately compensated (e.g. teachers and nurses) are frequently in positions in which they are government employees or are funded with government grants.
The power to tax is routinely used to impose taxes on economic gains which are deemed to be excessive, and tax breaks (deductions and credits and exclusions from income) are routinely made available in connection with economic gains and conduct deemed to be valuable.
For example, in the U.S., charitable and religious organizations are tax free, donations to them are tax deductible to donors and excluded from gift and inheritance taxes, and the implicit income from providing housing in kind to clergy is not taxed. There are also credits and tax breaks available for conducting research and development, for employing people who categorically often have a difficult time finding employment, for protecting the environment with a conservation easement, and for building low income housing. Meanwhile, some kinds of activities are more heavily taxed than normal, such as selling marijuana, retaining too much profits in a corporation not taxed on a pass through basis, using plastic bags at grocery stores, consuming alcohol and tobacco, and so on.
There are also "private law" and regulatory mechanism to address people who are perceived to make too much money based upon undesirable conduct. When the benefits are at the expense of someone else, we authorize the losers to sue the winners in the relationship.
For example, spouses often do considerable unpaid work for each other and their children in the course of a marriage. But if a couple divorces, the unpaid work is compensated for by assuming a "partnership theory of marriage" that divides property and awards alimony in a way that equitably divides the gains that the couple as a whole made economically during the marriage, effectively treating the unpaid work in the marriage as definitionally equal in value to the paid work in the marriage.
Laws mandating that decedents make minimum provisions for a surviving spouse are directed towards more or less the same end.
Similarly, discrimination law seeks to redress within a firm overcompensation of some workers and under compensation of other workers relative to each other for impermissibly discriminatory reasons by allowing the workers discriminated against to sue for money damages arising from this misallocation of resources for impermissible reasons.
Collective action by unions, through collective bargaining agreements and labor action to secure collective bargaining agreements, similarly tries to secure equity between different participants in the same firm.
On the other hand, the government finds certain criminal activity to be definitionally undeserving of compensation, and in furtherance of that prohibits people who are owed money in connection with criminal activity from suing to be paid what they are owed, and furthermore makes the assets of those people subject to civil and/or criminal forfeiture, and imposes fines on these people.
which mechanisms have been proposed to actually solve this perceived
problem and achieve wages that are aligned with social value
production (however one may define that term)?
This question seems to contemplate a global restructuring of the economy by one primary mechanism that aligns these things, and I don't think that this has been done or even seriously proposed outside of a purely communist regime (and even then, not really, as that often simply aspires to give everyone what they need without regard to whether or not it was earned).
I don't think that this is possible, in part, because the social value of particular kinds of production isn't easily established and is deeply rooted in normative judgments particular to each particular activity.
Instead, the solution, as ugly and messy as it may be, is to identify particular groups of workers who are overpaid or underpaid relative to their social value and craft solutions on a case by case basis, in much the way that the market valuation of work is not the product of some top down overarching single determination, but instead arises from, in an economy the size of the U.S., for example, billions or trillions of individually negotiated transactions each year.
If we think parents are undercompensated for their parenting work, we could subsidize parenting through taxes (as we do), publicly provide funding for obligations of parents (as we dod in public education), and could as a matter of private law impose duties on children to generously support their children (as historically was common as strong social norm).
If we think professional athletes or college football coaches are overcompensated, we could cap their salaries, or impose taxes specific to that kind of activity.
If we think teachers are underpaid, we could increase their pay by raising taxes to pay for it.
If we think investment bankers are overcompensated, we could more heavily tax earnings from capital and property than we do.
One answer proposes a national "maximum wage" but that doesn't do much to help the problem of two occupations where most workers are paid less than the maximum wage having the wrong wages, based upon social value, relative to each other. It may mute the impact of a few people being overpaid, in much the same way that progressive income taxation does, but it doesn't fix the relative incentives to pursue one line or work rather than another.
One could certainly commission studies to better examine which workers and activities produce positive and negative economic externalities. But it would be foolish to believe that such studies are not more art than science. Ultimately, someone has to evaluate those studies, find them to be credible, and come up with a workable way to reconcile the situation with the status quo on a case by case basis. Most likely the solution should reflect the nature of the economic externalities. Ideally, if people in one occupation imparts positive externalities on another group of people, we would tax the beneficiaries for the benefit of those providing the benefits.
But this can go too far. Suppose that you could perfectly account for all externalities and transfer funds so that net of the transfers there would be no externalities, positive or negative, in the economy. This would still mean that very capable people who do a lot and earn compensation would be very highly compensated, while people who are impaired in some way would receive little or no compensation, even though they need economic support to live. Lots of people are in the little current contributions boat: children, elderly retired people, people with disabilities physical, mental, or cognitive, and the ubiquitous category of unconnected people with bad luck whose unfortunate choices (whether justified or not) has led them to contribute little to society. Unless we want extreme social Darwinism, simply paying people based upon the value that they contribute to society, when some people are more able than others, is itself unfair in a different way.