I think you were very clear in your post, but it is generally easier to write what you feel than actually discuss it with someone. This is especially true for people who are bipolar, since a change in mood might also change the way you feel about other times. For example, when happy, some people feel like they've never been sad and don't understand why they remember feeling that way in the past. If you have trouble "not getting to the point" or forgetting points, I'd suggest writing down some dot points to take with you to your appointment. It sounds silly but it does help. There's more than just bipolar I and bipolar II. I think your "pleasant" moos swings do sound like mania or hypomania (which is slightly less extreme mania) which are common in most bipolar subtypes, but your "low" states don't sound like traditional depression states. Something a lot of doctors overlook is mixed state bipolar, where you get the high and low at the same time (though you can still get the high and low separately). This results in feeling depressed but also experiencing huge amounts of energy. This can be experienced as panic, aggression, and other things, while not actually being expressed externally because of the depression part that stops you acting or moving or going out. This is very difficult for a lot of people to understand unless it's been experienced, and it's only just being acknowledged in recent years. If you feel like this might be the case, mention it and your doctor will be able to talk with you about it. It would explain why you don't feel like the "classic" bipolar definition doesn't suit you.
Alternatively, if you feel like bipolar is too extreme of an illness to be applicable to you, other diagnoses like cyclothymia may be more suitable. CBT and antidepressants alone wouldn't work with bipolar. You need some room to think before CBT will take, which can be achieved with mood stabilisers, and antidepressants don't help with that excessive energy you might be feeling, or with mania. I'm not sure what applies to you since diagnosis is an extensive process, but I hope this gives you some idea of how to approach what you're feeling with your doctor.