Could Donald Trump run his presidency similar to Ronald Reagan if he's trying to recapture that moment?
Do you mean achieve the same level of success as Reagan did for the party? Because if so, then no. He's simply too offensive and while I do admit he will probably bring in more working class whites to the party (at the expense of other whites turned off by him), he flat out alienated the largest growing voter blocs in this country. Reagan didn't really do that. He wasn't offensive like Trump at all.
Trump's keen awareness of the GOP electorate / working-class in general is pretty great, but his deliver and strategy is too polarizing. At best he will get Republicans a short term boost in support at the expense of long-term damage.
However, policy-wise, aside from the immigration/muslim stuff, I do think he is helping to put the GOP on a path towards policies more suited for the voters needs or desires, and not only the donors, which has historically been the case
(and exactly why the voters are infuriated with the GOP establishment now)