Since you've already punched the 121 ticket, that helps for future progression to majors.
Normally it wouldn't look good in the eyes of majors for a regional pilot to switch to 135, especially if you're still on probation (they might think you were asked to leave or didn't like the lifestyle). But you got furloughed, and COVID, so I'm sure that would be fine under these circumstances.
But as you said, the safest path to 121, is 121, especially 121 TPIC and ideally LCA or sim instructor.