You are right in saying that hinduism spread in south east asia because of conquest.
The conquest of south east asia was by a chola king (a shivite). Even now the budhism practiced in Thailand and areas around has a very much shivite influence.
But unlike Islam, Hinduism did not have missionary zeal. When cholas collapsed hinduism veined in these regions. As described above, their influence still persist in some part of these areas.
Portugese had a very missionary appeal to their conquest while British was mostly secular. The Turk and Persian invasion also had a very missionary aspect to it. The respective missionaries had a lot of help from the patronizing powers. This is why Christianity and Islam survives to this day in India. They were organized and even when their powers weakened the missionaries could continue their work (because of secular British). But these missionaries would not have been here in the first place if there was no invasion.
India was mostly Budhist till Shankarachary came along to revive Hinduism. India would have been budhist if there was no Shankaracharya.