Is it a good idea to keep your home timezone sleeping pattern when traveling to a far timezone?

I think 3 hours is the most I would be prepared to be "out of sync", unless I was only going for a weekend. Presumably the reason you are traveling is to work with people in person, not to sit alone in your hotel room from 11pm to 7am local time getting in a full day's work, then head out for a little sightseeing and a few beers at 8am. (Or if it's the other direction, working from 7pm to 3am and then catching a few sights and activities.

You might be able to do some strange things like getting up 4 or 5 hours before you need to, doing some personal things, then working and going straight to bed, but you will miss out on the opening hours of most leisure things you might want, on the daylight to see the sights, and on the time of day they serve dinner in the restaurants.

Two tips for you. First, learn to sleep. You should sleep on planes. We've had some questions here on it, but it's mostly about equipment: pillows, lightweight blankets, ear plugs, noise cancelling headphones and a device that plays music, etc. Under some circumstances, you can also sleep in airports - bring your own alarm clock from home if you're afraid you won't wake up. In fact, learn to nap in general and how to wake up after a short one. This is something practice will make you better at.

Second, learn to adjust to a new timezone or start to pre-adjust before you go. Anxiety makes it worse, and can lead to some really bad decisions like staying up for 48 hours, so practice and get better at it and more comfortable at it.