You can use card to flip it face down to free the zones but careful cuz when flip back up, the owner can select zones to lockdown again. Soul exchange work because it will be removed form the field 1st and free the zones to let you summon a tribute monster.
this just happened to me!
my opponent played cyber-stein and paid 5k life in order to summon ojama king on 1st turn (the guy had mai's LP boost) and lock my 3 zones
luckily i had a wall of disruption on my initial hand so i could set it up and make all his 3 creatures atks turn to 0
i won this duel cuz i run 23 cards in my deck and my opponent only ran 20 so he concedes b4 deck over
Cyber stein with 5k lp then another summon with life cost 0. It is possible to get OTKed unless you have wall of disruption, a monster already on the field, or a Drowning mirror force.