The OP said, in the OP, that he lives in Ohio.
Virginia sounds like they have some issues. In Ohio, your insurance company will likely send info to the state saying that you cancelled your insurance, and there is a chance that you may get a postcard in the mail telling you to send in proof of insurance, or proof of no longer owning the vehicle. That is why I advised keeping the receipt handy. Also, keep an eye out for the postcard, I have never received one, but I have heard that some people have missed them, as they look a bit like junk mail.
Also, conveniently in Ohio, your plates expire on your birthday, so you don’t need to rely on the state to contact you to remind you when your plates expire, so the rest of your story that came about because you forgot to renew your plates is not as pertinent.
We have no penalty for not registering a car, only a penalty for registering a car late.
If the OP wants to keep his plates for the new car, then that’s a bit more complicated, and would need to be done before the registration on the old plates ran out. As plates are only another few bucks ($12 IIRC), the only reason to worry about that is if you really like the #, or don’t want to have to remember a new one.
I’ve been an Ohio driver for 23 years, have changed vehicles several times, and have never been asked to surrender my plates(I am pretty sure they only do that when you have certain types of infractions, DUI and the like), never had anyone give me a hassle about not registering a car that I do not own any longer (or even cars that I did own, and hadn’t bothered to get junked yet, as long as they were not driven or parked on the street.) The only gotcha that you really need to be aware of is the insurance angle, in that if you have a registered car without insurance, you can get into trouble about that, and as the OP’s registration is about to expire, that’s not all that big a deal either.
I am also surprised that your insurance went up. You should look into a better insurance company, if you have one that increases premiums for non-driving related infractions. Maybe it’s a Virginia thing, but Allstate in Ohio would not raise rates over those sorts of bureaucratic shenanigans, only for driving infractions.
I am not sure how this would work. If you get a ticket or in an accident, it is the driver of the vehicle on the hook, not the owner. Even if he was still the whole owner of the vehicle, and it was lent to a friend, he would not be responsible for them. Traffic cameras or parking ticket citations may go to the owner of the plates, but if the plates have been removed from the car before it is towed (something that the tow guy will offer to do for you if you have not already), then that’s not really an issue either.
One quick suggestion to the OP, I would suggest donating to goodwill. You might get a couple hundred off of a cash for junker outfit, but then you have to go and do title transfer and notary stuff yourself. With goodwill, the driver takes care of all the paperwork, all you need is your title and a pen( and the driver probably has a pen as well). If your car sells for more than $500, they’ll send you something for your tax records. Depends on how much you think you will get for it, and whether that was worth the hassle. Also, the cash for junkers guys are usually a pain to schedule, last time I tried them, they wanted 2 weeks before they would come out to give me an estimate. Goodwill picked it up the next day.
Also to the OP, if you walk in with your plates, they will take them from you. They won’t consider it to be all that terrible a thing, they’ll just destroy them themselves. And, in my experience, the tow truck driver from goodwill has temp towing plates to throw on the car. I don’t know all the details of how that works, but he seemed like he was happy with it.