You can rent a compression tester for free from the auto parts, how it usually works is you pay a deposit and then you bring it back within 2 days for a full refund. Basically the consists of removing the spark plugs, threading the compression tester in, cranking the engine until you get a reading, and writing it down to see what the compression is. I don't know the spec for compression on a Honda Accord but they should all be pretty similar - if you have one or two that are far lower, you've found the problem. I also don't know if the plugs are hard to get to on this car, but you should be able to find a YouTube video on that easily enough.

Something to keep in mind is that while head gaskets can fail over time, especially on older or high mileage vehicles (by the way, how many miles do you have?), it's common for other cooling system problems to cause it to overheat and that kills the head gasket. So, a bad thermostat could have been the original issue, and when you let it overheat, it took the head gasket with it. Could have also damaged the cylinder head or engine block in the process, but you don't really know at this point.

Stuff like Bars Leak head gasket fix could work, as long as you follow the directions, and it's worth the few bucks to try it. There's always the risk of possibly clogging something else, or causing further problems down the road, but you quite possibly have to pull apart the engine anyway, so no need to really worry about that.

Your P0117 code is either a problem with the coolant temp sensor, or it could be triggered by air bubbles/lack of coolant. Either way, it's not causing your problem, so don't worry about it. Your P0122 code also doesn't have anything to do with the cooling system, though it could cause the car to not run quite right, but at this point that's irrelevant.