I rather doubt that it can be considered progressive. The entire program of the Progressive movement was reform. The mantra of the movement was that the cure for the ills of democracy are more democracy. Although two Presidents, Roosevelt and Taft, might be considered progressive, they were not typically conservative. Roosevelt went after big business with a vengeance in his "trust busting" campaign. His activities upset J.P. Morgan so much that when Roosevelt went big game hunting in Africa, Morgan commented, "let every lion do his duty."
Big business was often the target of the movement, not its darling. At a time when a high tariff would have supported big business, President Taft worked for a lower tariff. The progressive movement also supported the nomination of candidates for political office by primary. The old system, nomination by convention, allowed party insiders to control matters. Additionally, the 17th Amendment was passed which provided for direct election of Senators.
I'm not sure where the idea came from that the Progressive movement was conservative; but anyone who argues that position, in my humble opinion, is fighting a losing battle.