Best method is setting the anchor up to "trip" using the ties as you have mentioned but unfortunately, sometimes it doesn't matter what you do your anchor is going to get stuck. I use a Sarca and have never had an issue but I have heard of them getting caught on the odd occasion - they're not the cheapest chunk of steel to lose. I have heard of people breaking bowsprits as well. The Seafarers is held on with sika and 4 countersunk bolts ( at least mine was) underneath the stainless chain guard. I dismantled mine, re did the sika bedding using a lot more sika ( It will be a shiteload harder to get off next time) and added 4 more bolts.
You could try using a traditional reef pick with some lighter tines but even these on occasion will get hung up and not want to come back (had this happen personally). We used to do a heap of diving for crays when I lived in Perth - once I managed to drop my pick straight down a chimney into a limestone cavern that was about 5 metres deep. Wasn't an issue with diving as we just went in and got it out (along with a few critters) but without the scuba that pick would have stayed there permanently as well. Ultimately the best way to not get them stuck is to anchor out off the edge of the structure and either let out more rope or fish lighter and float your baits back onto the spot - this can be tricky in areas like Harry's though due to boat traffic