A few things jump out to me here:
30-40% bodyfat isn't great health. It mightn't be killing you right this minute, and currently your body might have its shit together (blood pressure, resting heart rate, cholesterol levels, etc) but over time that'll change. So your doc is spot on, you need to lose the fat because it's a timebomb.
Setting calories that low to start is a bad idea because it'll suck horribly. You'll drop weight fast for a short time and then stall. At 280 lbs your maintenance is between 3900 calories/day and 4700 calories/day without taking into account body composition. Nonetheless, even then 3500 cal/day would very likely kick you into losing weight slowly. Now, your lean body mass is around 182 lbs (280x0.65, given your bodyfat is 30-40%). Maintenance for your LBM is between 2500 and 3100 calories. That 2200 calories is a significant deficit even for your LBM. If you drop your calories to that low a level, it becomes a free for all in terms of what your body uses for energy and you'll most likely end up losing muscle almost as much fat.
High cardio is probably unnecessary. If you can walk briskly for 30 minutes each day on top your barbell work, you should be sweet. As you get used to it, add time, pace or load; or start adding in a session of shorter, higher intensity work. Keep training to get stronger, but try shortening your rest between sets and maybe do some higher rep work at moderately heavy loads too.
Low carb may well be the way to go, because it does seem to work well for people with higher bodyfat. Personally I would think if you set you calories at 3400 per day to start with, you'll be in a good position. That's 500 calories below the low end maintenance for your scale weight and not much above the top end maintenance for your LBM. This gives you PLENTY of room to adjust calories down without risking muscle retention.
Very broadly, I think you would do well to start at 3500 calories and get around 70% of them from lean meat, vegetables and good fats (olive oil, eggs, avocados, etc). That other 30% get from complex carbs (oats, rice, yams, potato, etc). On average, shoot for your scale weight to go down about a pound a week. When that stops happening, drop your calories to 3300 per day, and when that stops your scale weight dropping go down to 3100 calories/day, etc. Use the mirror and tape measure too. If you look leaner and your waist is smaller, you're on the right track even if the scale isn't moving.
Once you hit around 20-25% bodyfat you might find you do better upping carbs and dropping fat, but you may not need to.