I would recommend a combination toaster and convection oven. While I have a regular oven in my small apartment, I rarely use it in favor of saving energy (and money on my energy bill) by using the toaster/convection oven. I have purchased toaster oven sized muffin tins (just a 6 muffin tin) and a toaster oven sized roasting rack that fits two sizes of meat. My oven came with a roasting pan. The convection features have done wonderful things for my pies. You can get them big enough to make pizza in. As long as you aren't cooking for a crowd, it will work wonders. Things I've successfully baked in there include:
- Muffins
- Cake (did have to do it one cake at a time for a layer cake)
- Pie (the convection feature is perfect for pie!)
- Bread
- Cupcakes
- Pitas
- Steak (well, it was a broiled steak recipe - the best I can do without a grill)
- Chicken breasts
I had a friend who rented a place that has a convection cooking setting on the microwave. We successfully used it to make muffins once, but I haven't tried it further.
Short answer: They're probably not safe.
Unlike "microwave safety", there isn't a safety risk in contaminating the food contents of the jars due to heating in an oven; in this case you just run the risk of the jars breaking.
I am not sure what the symbols on the bottom of your jar mean; (see edit below) from what I understand—unlike plastic resin identification codes—there isn't a standard set of symbols for glass. Those symbols likely represent the manufacturer, production date, and patents.
Unless glass is processed in a special way, it is prone to breaking when it goes through rapid temperature changes. Therefore, if your glass is run-of-the-mill soda-lime glass (which is extremely likely), and if you were to put it from room temperature directly into a 450°F oven, the shock of that rapid temperature change would likely crack it. Furthermore, even if you were able to gradually heat it up to 450°F without it cracking, it would likely crack even as it naturally cools down. In order to try and ensure that the glass doesn't crack you'd have to both gradually heat the jars up and then very gradually step the oven temperature back down to room temperature.
If you want to use glass, your best bet would be to use something like Pyrex.
Even Pyrex, which is explicitly designed to be oven safe, can't withstand the direct heat of a broiler, though.
Edit: I believe the symbol on the bottom of your jars reads "A.G.C." surrounded by the outline of the state of Arkansas. This implies that your jars were made by the Arkansas Glass Container Company. I believe the numbers indicate the model number, which appears to be this jar. AGC unfortunately don't have anything on their website listing the oven safety of their glass. If you're really interested, you could try contacting the manufacturer.
Best Answer
The whole "baking at altitude" thing is a beloved kitchen tale, but usually completely irrelevant.
Certainly, the different pressure is a reason why the same physical changes in baking happen at a different temperature. And 8000 ft is nothing to laugh at, there water boils already at below 80 C instead of 100. So, you're dealing with a difference of ~20 degrees Celsius. This is indeed a number to behold, as opposed to people who start talking about high altitude baking at 900 ft.
But what is much less known: Ovens are not a precise cooking method. I've regularly seen ovens which differ by over 40 C from the temperature shown on the thermostat. I've also regularly seen ovens where the difference in temperature between the back right corner and front left corner was at least 30 C. My grandma's oven doesn't even have degrees on its thermostat, just 6 settings. My other grandma and all her sister use a wood fired oven and regulate temperature by sometimes shifting the coals or throwing another log on. From ancient Sumer until the mid-twentieth century, humanity has baked without thermostats. And did so at all altitudes too.
When you moved, there are many variables which changed which might have made a difference on your baking. The difference in average oven temperature is one, but it could also be anything from a different flour type (flours which are considered "bread" in some parts of the USA are labelled "AP" in others) through maybe having bought a new cake tin because the old one was too scratched to take along on the move, to you being stressed out, making small mistakes sometimes when baking and then falling prey to confirmation bias (you think your baking has gotten worse, and only notice the times it turns out worse than average). There is no way to say what happened.
The key here is that there are two types of baker. One learns to follow process to the t. She uses the same utensils, the same ingredients, then sticks the cake in the oven at the usual temperature and sets the timer. With a few iterations, she has her process perfect, and starts producing successful cakes, then everybody is happy. But, if for some reason something changes, whether a known or unknown variable, a controllable one or uncontrollable, everything goes out of whack.
Then there is a baker who pays more attention to what is happening, and why. This baker might be interested to read a bit about the physics and thermodynamics of cake batter. Or maybe not even that. But this baker will experiment a lot, pay attention to the difference. And this baker will never just set a temperature and a timer and go away, unless replicating something she did a dozen of times in the same setting. This baker will observe the batter before baking, and then in the oven. And no matter if it is the first or thirtieth time baking the same cake, she will not care what the clock says. She will use her nose to decide when to start checking the doneness with a wooden pick, and take out the cake as soon as she observes that it is done, not when she has waited the "magical" amount of time. This type of cook is unlikely to have to adjust anything when cooking in another place, be it with a different altitude, different oven type, or whatever.
To your specific case: there is no need for a new oven. Any standard oven should be usable for baking cakes at any altitude found in Virginia. You just need to find out what it is that your cakes need - longer time, lower temperature setting, less baking powder, more baking powder, or something else - depending on exactly what goes wrong during making them. Without us being there and observing the signs, we can't tell which it is. From the scant description you give, "nearly raw in the middle", I'd suggest reducing the temperature as a first thing to try. And in any case, throw out your timer. It is convenient for your personal time management in the kitchen, but simply inadequate for deciding when to take a cake out of the oven.