The newer Verizon plans have what's called "Safety Mode" - when you reach your plan allowance, the data slows to a crawl (but is probably ok for email checking) and there is no overage charge. You also have "Carryover" data; any unused data from the previous month is added to your allotment for the current month. BUT, you need to be on the new Verizon S, M, or L plan, and those data allotments are 2, 4, and 8 GB.
How much are you paying for the 6 GB now? Check the pricing on the new plans, and see what the difference is. Another factor to account for is if the phones you have a re on a device payment plan, or paid for, on on contract. That will make a difference in the line access fee for each line, so you really need to do the math and figure what is most cost effective. You can change plans at any time with no penalty.
As to your original question, can you stop the data at 6 gb and avoid overages, the answer is no, not through Verizon, You would need to do it yourself by turning off the phones - and there's no guarantee that it would work, since some data may be reported at a time you don't expect, especially if yo a re trying to time it to the end of your cycle.
