Dealing with stress in competition is one very important aspect of a well-rounded preparation strategy. I think that the most crucial point in answering your question is actually contained within the question itself:
"These games share one trait: I have plenty of time to think about what to do before making a move. On the one hand that's great since it makes the game independent of reflexes. On the other hand I have plenty of time to stew over how I might be making a massive blunder."
I'll assume that either you are faster than Magnus Carlsen at thinking, or that you tend to play longer games. Since most of us do not think about chess faster than Carlsen, I'll go with the "longer game" option. This makes things quite a bit easier than if you were playing Blitz, Bullet, Lightning, or Armageddon games. There is enough time on the clock for you to do a self-assessment, get a grip on yourself and direct your thoughts appropriately - if you know the tricks of how to do so.
Here are a few things that I've found to be helpful.
- Breathe properly.
Most of us, when stressed, will naturally hyperventilate (breathe too quickly). We then blow out a lot more of the CO2 in our blood than we normally would, out into the atmosphere. Our bodies actually use the concentration of CO2 in our blood to gauge how much oxygen we're getting, so it thinks that because we have a low CO2 level, it means our tissues don't need that much extra oxygen even though we do. What happens next? Our body sends even less oxygen to our brain than before, because our hyperventilating has tricked it into thinking we don't need it! We then stress out even more because our brain is now lacking even more oxygen. This cycle goes on and on, and our performance suffers more and more because of it.
How do we fix this problem? We need to find a way to allow our CO2 levels to come back up so that our body transports more oxygen to the brain.
Many people who need to perform at their peak have adopted a strategy developed by the military that goes by many names: For the sake of what we're doing today, we'll call it "Box-breathing." It is incredibly simple, and if we apply it when we're stressed, it can get our physiology back to doing what it should have been doing all along. I personally have found this technique to work even better if you focus on keeping good posture and relaxing your neck muscles.
The technique:

Use Box breathing before, during, and after your games. Give yourself reminders until doing so becomes a habit.
- Take care of your physical condition
Chess is a sport, and participants of a sport need to take care of their bodies. Think about the heart muscle; if you're in average shape, it will pump nearly 4000 times in an hour to deliver oxygen and nutrients to your brain and body, and to take waste products and CO2 away. Your heart rate is intimately connected with other aspects of your physiology such as breathing rate and stress level. What would happen if your heart could pump the same amount of blood to your tissues during a chess game, but beat fewer times while doing it? Your stress level would go down to an even more manageable level.
How do you achieve this fitness? By exercising your heart muscle. The Mayo Clinic recommends that we all reduce our time spent seated, get a bare minimum of 30 minutes per day of physical activity, do strength training twice a week, and get at least 150 minutes of moderate aerobic training, or 75 minutes of vigorous aerobic training in a week. This guideline is a minimum.
Indeed, I recommend testing yourself once a month with some easily standardized test such as the 12-minute Cooper's Test: You run for 12 minutes, and write down how far you went. Then, set a goal for next month, and train accordingly. Focus on small, consistent improvements in physical fitness - it will certainly show in other aspects of your life, too.
Another recommendation is to cut out refined sugars, simple carbohydrates, and processed foods from your diet; replace them with things like green, leafy vegetables, and drink plenty of water. Not only will it help you in your fitness goals, but it will also keep your blood sugar consistent, and keep you from getting heart palpitations and high stress at the most inopportune times.
Stick to a manageable eating schedule, and see what works for you during periods of stress. Bring something appropriate with you to tournaments.
Finally, make sure to get enough sleep. It will make your chess practice more efficient due to the fact that you move information from short-term to long-term memory while you sleep. It will also help to clear your body of toxins. It works even better if you consume one cup of water before going to bed.
- Don't think about a blue elephant
Gotcha! I'll bet you thought about a blue elephant even though I told you not to. Don't worry; we all do. Interestingly, the fear of failure works in a similar way. There is a healthy way to hate losing, and there is an unhealthy way. The healthy way is to let it be a motivating and directing factor to mold your practice in an appropriate way. The unhealthy way is to stew over making a massive blunder, thus interfering with your decision-making in game.
In game, I highly recommend going back to "Box breathing," and once you've gotten yourself in a better frame of mind, go back to your game plan. This, of course, means that you must make sure to have a plan going into every game, both for how you will take care of your psyche, and how you will play with the pieces and chessboard. This leads directly to point #4 which is:
- No matter what the tournament is, your primary goal should always be to improve.
You've done your preparation, you're healthy, you're well-rested, you're breathing properly, and you're ready to go. All you can fairly expect from yourself is to do your best. There will be time to analyze your games after the tournament is over, and improve for the next one. No matter what good moves or blunders you may make through the course of the game, keep your focus on the present: Don't disregard your plan for flashy moves that are tempting, but after calculation show that they don't actually improve your position or further your plans in any way; don't lose your cool when your opponent plays an unexpected move.
Do your calculations, move your pieces, and play your best. On tournament day, keep your focus on playing good chess, and save your game analysis for whenever you get enough time to do so peacefully. If you start getting the urge to beat yourself up over a loss, or unduly congratulate yourself for a win, give yourself permission to do that in another time or place. Right now, you're in a tournament. Observe your opponents' strategies and consider how to defeat them. Play your own strategies and focus on your strengths. If you've properly done the previous three points, you will be in a good position to do so. Give yourself gentle reminders as necessary, or even better, recruit someone else to come with you, bring drinks, snacks, and be a support for you.
I hope this helps.
In summary:
Breathe properly
Take care of your physical condition
Don't think about a blue elephant
No matter what the tournament is, your primary goal should always be to improve