Given the number of years and the number of participants affected by the failures, you should file a VCP. There are operational and document failures. After a closer look, you may find demographic failures, too. The DOL alone cannot address this range of issues including the document issues.
The reporting of late deposits on 5500s is cumulative which means you add each year's late deposits to this year's late deposits and report them until they are fully corrected.
Similarly, the 5330s are cumulative with each year added to the next year's 5330 until all the taxes are paid. Essentially, you pay each year's tax over and over again until there are no more late deposits associated with that year.
Filing amended 5500s once this is cleaned up is a good idea to formally set the record straight. The 5500s are used by the agencies to identify plans with deficiencies so not amending them is inviting future agency reviews, audit or investigations. The amended returns supersede that prior filings.
Note that when the plan files the VCP, the expectation is that the VCP will cover all deficiencies. Take time to look at employee census data for each year. You may find failures to implement deferral elections, missed deferral opportunities, ineligibles getting contributions, eligibles not getting contributions, unpaid benefits, unpaid RMDs, and more. The process not only will involve fixing participant accounts but will also communicating to the plan sponsor and to participants what is happening inside the plan.
Be sure to prepare a service agreement documenting your fees to do this work, and include provisions for progress billing throughout the engagement. Plan remediation over a long period of time compounds the effort needed to get a plan in compliance.