In article .com,
says...
Whoops, "It" could be treated in said manner.
Also, fibreglass bath with wood inside the rim.

I know you said you don't want metal brackets, but you could do it by
fixing a thin strip of angle steel to the timber on the bath, with the
flange projecting above the edge of the bath, then screw that onto the
wall and tile over. Or similarly but using 12mm ply instead of steel,
remove the plasterboard from that bit of wall and screw onto the studs.