State lawmakers have begun advancing a pair of bipartisan proposals aiming to speed up unemployment payments for out-of-work New Jerseyans after the state’s system received a wave of criticism during the coronavirus pandemic. The state Senate Labor Committee on Monday approved one bill (S2357) that would make a series of changes to how the state Department of Labor handles unemployment benefits and another (S2396) that would require the department to deliver an annual report on its performance responding to unemployment claims. Sen. Fred Madden, D-Gloucester, the committee’s chairman and a mai…