On another product we "solvent welded" parts together using granules of raw plastic "melted" or "dissolved" in a 3M's solvent. This was painted into the joint to fill/stick/weld/seal the joint. Similar to the solvent cement used on plastic waste pipes except we dissolved plastic the same colour as the mouldings.
The raw granules are sold as product know as 'polymorph' and can be bought on ebay etc although it is sold as a moulding plastic it can with lots of practice , or luck as a bonding agent the main problem with using this method is that the polymorph has to be heated to an exact temp and kept at that temp whilst moulding so its not a great product for home use.
Best method for DIY would be a a plastic cement as said similar as used for pipe work. as with any type of welding the type of joint (Lapping/ butt/ folding) when done properly will dictate the strength.