I had one of these toddlers!! He was too smart for his own good! For some things we actually went to using locks to keep him out. We would then just put the key nearby but out of his reach or climbing range. It was a pain but it kept him safe from himself without me getting too many more gray hairs!
They have locks with a long shank/hasp/shackle like that, but the body of the lock slides up to secure the clasp tightly. I don't know if they'd slide far enough to fix your problem though.
Couldn't a hacksaw or crosscut wood saw go through that plastic in about sixty seconds though?
Lmatfy - Master Lock 527D Padlock, 5/16 in Dia, 2-3/8 in H X 1-1/32 in W, Brass Black https://www.amazon.com/dp/B0002YP5U4/ref=cm_sw_r_cp_apa_i_Bj-UCbBKQAP2V
Maybe something like this..
Master Lock 527D Padlock, 5/16 in Dia, 2-3/8 in H X 1-1/32 in W, Brass, Black https://www.amazon.com/dp/B0002YP5U4/ref=cm_sw_r_cp_api_i_bhe9DbF3SKQB8