I was overlooking a lot of option when i first started, sure the godess shrine will help you for a price, but keeping submissiveness low will keep the ghost friendly, have a faction on your side or freeing prisonners will give you allies you can keep at the beggining of the level to once again help with tough restrains.
the best tip in my opinion is to customise your run. a lot of perks helps to get free, and getting a head start on getting stronger will prevent you from getting stuck in 20 restrains in the first place.
thief if i recall correctly, with all the right perks, if very hard to get soft locked. asking for a restrain from a roaming NPC can refresh the 12 turn of very strong struggling that stack with the 4 escape artist, that stack with willfull struggle, that stack with.... you get the idea.
mage can cast will all but the strongest gag and muzzle witht the right perk too and you have spells to unlock yourself. look for a way to sustain mana and it become hard to become soft locked.
one of my most enjoyable run was with bound crusader, where accepting quest would lock me in 3 random restrains until the quest completion, mage witht he right perk and spell selection is rarely out of option to complete the quest, and you can use the point for perks like using keys even with bound hand for exemple, wich is a nice safeguard if you have trouble keeping friendly npc around.