While you could try a vertical, if you have that much height available then
a horizontal antenna high in the trees will likely do much better.
Let's start by defining an objective: we can look at an Azimuth map based
on New Jersey using NS6T's website here: http://ns6t.net/azimuth/azimuth.html
India spans from 15 to 40 degrees; Vietnam and parts of Indonesia are due
North; Australia spans about 250 to 330 degrees, and New Zealand is
around 245 degrees. And, of course, roughly the opposite directions for
long path. It sounds as though your current antenna is working well for
more North/South paths, while an antenna that fires East/West will give
you better coverage of the East coast of Australia and New Zealand.
One simple approach is to make a half-sized version of your current
antenna and string it up between two trees about North/South: maximum
radiation will be broadside on 20 and 15m, and a multi-lobe pattern on
10m. Actually you can shorten it somewhat: 40' or so will give you a
broadside main lobe on 10m and all lower bands. As long as it is at least
a half wave on the lowest main band of interest (say 17m or 15m in this case)
then it will work well on the higher bands and can be pressed into service
somewhat lower in frequency if desired.
Another option is a vertical loop. Probably the easiest would be a delta loop
with the point down, fed at the bottom using open wire line. A full wave
loop for 15m will also give broadside radiation on 12m and 10m, and can be
pressed into service on 17m and 20m. That requires less than 20' of horizontal
space between supports, which may give you more options of how to place it.
You have enough height that there may be an advantage in using a broadside
array: two straight wire radiators spaced perhaps 20' to 25' apart vertically
(one under the other) and fed in phase with ladder line: that gives you some
gain at low elevation angles. The wire lengths would be as discussed above.
Otherwise there are various types of colinear, arrays, etc. that can be hung
between the trees with more gain, but you do need to be careful because more
gain in one direction comes at the cost of less gain in another, where you may
also want to make contacts.