MY technique is along the lines of Birds comments, I have done just about everything. Haven't brush hogged since 5:30 this PM so can remember what I did.
I can go CW or CCW but like all drivers trained to sit on the left side when steering a car, I feel more comfortable turning left. I ordinarily DO NOT raise the cutter when turning, I'm too busy turning the wheel. I find with my short wheelbase Kubota Grand L-4610HSTC with 6 ft Cimmaron mower that if I turn the wheel sharply at the right moment, even when traveling pretty darned fast, the mower kicks out and gets the part you'd think you'd miss and produces a good square corner.
When dodging a fruit tree or whatever, on subsequent passes I tend to NOT follow the curved path used to dodge the obstacle . I only re-cut a very small amount and the subsequent passes are soon rectilinear again. With the HST it is trivial to stop and backup so if conditions, including a plain old fashioned OOPS, warrant it you can easily back up to get a missed spot and then proceed ( I have two large rear view mirrors.)
After the remaining uncut target area is reduced to a small size where continuing a 4 sided race track pattern is inconvenient I will often alternate between backing up and going forward with no real turns just a little bobble at the end of a pass to line up for next pass. This is much more efficient than making a continuous forward effort and lots of turns where you are mowing where you have already mowed.
Often you may want a nice square corner but for some reason don't have room to make say a good 90 degree left turn (or your setup doesn't make good square turns.) A 270 right turn will get you there the same. Just run a bit past the point where the left turn would have been made and then make a hard right 3/4 of a full circle and you are lined up again where you want to be.
If for some reason you want to retrace your path in the oposite direction and not back up you can make a 90 degree turn and then an immediate 270 degree turn in the opposite direction and you will be going the opposite direction from where you started the maneuver with little or no positional or heading error so no bobble in your cutting path.
A harder skill to learn that requires more judgment than the 270 or 90-270 turns is a tear drop turn. A tear drop will also put you back over the same ground you just covered but going the opposite direction similar to what the 90-270 did. To accomplish the tear drop turn you turn 30 degrees from your initial direction and maintain that for a brief period (TBD by experience and the characteristics of your equipment.) You then initiate a turn in the opposite direction from the initial turn and continue that turn until your experience tells you to straighten the wheels. After the wheels are straight yo should be closing on your initial path (followed prior to initiating the teardrop turn) at a 30 degree angle. You then turn to track over the original path preceding the turn but in the opposite direction.
The tear drop turn is neat but just isn't easy for everybody. The 90-270 accomplishes the same thing and is purely mechanical with little or no experience or judgment required.
I have hydraulic TNT and find that it makes mowing under varied conditioins much easier. Today I mowed the right of way between one of my 1/2 mile long fences and the gravel road. There are ditches so when making the pass nearest the road one wheen is in or near the low point of the ditch and the other side is on the road. A quick adjustment of the tilt and you can mow close without a frequent contact with gravel when you hit an irregularity. I typically mow with the tail wheel in contact with the ground.
My brush hog does not have a pair of round holes to accept a pin to attach the hydraulic top lift. It has a pair of slots. This allows the mower to "float" along following the contour of the ground. If I back into a pond dam the rear of the mower is free to rise (although in extreme cases you would want to raise the hydraulic top to help out.
When I first got a rotary mower (brush hog "Bush Hog") I tended to set it too low and plow with one or both of the rubbing strakes. Now I typically run it just above the point of contact. Of course it still hits once in a while. Running with it NOT in continuous contact prevents furrowing the surface when it is soft and makes for neater easier hard turns.
Bush hog is a brand name. Brush hog is a generic term for a particular type of rotary mower. Kleenex is one brand of facial tissue but through loose usage Kleenex is widely accepted as a generic term for facial tissue. Likewise Bush hog which is a registered trademark and brush hog which is not Bush hog is becoming a generic term through usage.
Pat