I think the real answer to the question "How is Ronald Reagan a conservative, if conservatism means to conserve the status quo" is simply that he wasn't one. While the answer linked provides a reasonable definition of conservatism, it does leave a good deal out. The Stanford Encyclopedia of Philosophy article that that answer itself cites has this to say:
It is contested both what conservatism is, and what it could or ought to be—both among the public and politicians, and among the philosophers and political theorists that this article focuses on. Popularly, “conservative” is a generic term for “right-wing viewpoint occupying the political spectrum between liberalism and fascism”. Philosophical commentators offer a more distinctive characterisation. Many treat it as a standpoint that is sceptical of abstract reasoning in politics, and that appeals instead to living tradition, allowing for the possibility of limited political reform. On this view, conservatism is neither dogmatic reaction, nor the right-wing radicalism of Margaret Thatcher or contemporary American “neo-conservatives”. Other commentators, however, contrast this “pragmatic conservatism” with a universalist “rational conservatism” that is not sceptical of reason, and that regards a community with a hierarchy of authority as most conducive to human well-being (Skorupski 2015).
— Andy Hamilton, “Conservatism”, para. 2
From that, it is clear that if you believe in the definition of conservatism in the narrow sense, of being anti-utopian and opposed to radical change, Ronald Reagan's tax cuts were not at all conservative. Instead, by the narrow, technical definition, Ronald Reagan was a "right-wing radical" much like Margaret Thatcher would be. Right-wing, because of the laissez-faire principles, and radical because it was a transformation of the fundamental principles of economic policy at the time, not because it would have been particularly extreme. Reagan is called a conservative because of the popular and generic definition, of "any right-wing viewpoint in between liberalism and fascism".
Reagan cut taxes twice in 1981 and 1986, true, but those cuts were mostly ineffective in curbing spending, and he ended up signing multiple tax increases and cancelling many cuts as a pragmatic compromise. [3][4] His increases in defence spending drove the budget deficit to balloon anyway. He failed to abolish the cabinet-level Departments of Education and Energy as he campaigned for, instead he created the Department of Veteran Affairs. [5] His overall record in terms of limiting spending is not that successful:
As Lou Cannon observed, Reagan's own friend George F. Will, a conservative, "calculated that the middle six budgets of the administration had produced deficits totaling $1.1 trillion and that Reagan proposed thirteen-fourteenths of that total. Congress had added a relatively insignificant $90 billion...."
— Robert Erwin, 2001, "Regan in Retrospect", p. 379 Virginia Quarterly Review 77(3)
The theory of "supply-side economics" used to justify those tax cuts as increasing revenue wasn't exactly a sign of great scepticism towards theoretical reason either, and opponents like George Bush famously called it "voodoo economics". [7] Nonetheless, Reagan's policies marked a radical transformation of the fundamental principles of economic policy, and only after Regan can those policies really be considered conservative, under the narrower definition.