Did a little digging for you.
As you now realize, you should never buy a combo modem and wireless together because when one piece goes down, the whole device need to be replaced. Best practice is to buy a separate wired modem and wireless router. smallnetbuilder is the best place for current recos.
With your 6300, it is a 8 x 4 modem which is pretty old at this point (meaning 8 downstream channels and 4 upstream). Recommended is to have at 16 downstream. If you really want to futureproof, you can get a DOCSIS 3.1 Modem which is what is needed for Gigabit download. A good 16 channel modem is a Arris/Surboard 6183. You would need to buy a new wireless router for WiFi coverage.
You are correct that Comcast pushes out modem updates. Netgear and other manufacturers release their updates to ISPs and the ISPs test, validate and then release.
Another resource to check your modem levels is: http://www.dslreports.com/faq/16085
They also have an active Comcast ISP forum here, that you can post your problem to as well as your signal levels: https://www.dslreports.com/forum/comcast
When you internet goes down, you should test both the wireless connection and a wired/ethernet connection.
Lastly, if Comcast is blaming your equipment, you can always rent a Comcast modem/wireless gateway for a month and if you still have issues, make them look upstream. That can buy you time to buy a new modem and wireless router.
If you run into issues with the Customer Support, PM me.