I would really appreciate some advice from the experts here. I apologize in advance if my descriptions are unclear. Sorry!

Our ranch style house (on slab) was built in 1961. Roof (for vent access) is metal so footprints void warranty. Pipes are 3 inch cast iron. No external cleanouts except one small one outside kitchen sink. At one end of the house is bath#1 and a clothes washer that is right across from that bathroom. The sewer line then runs straight from bath#1 with feed from the kitchen sink and then stops at bath#2. The toilets for bath#2 and #3 are back to back but separated by a wall. Then it pivots and runs out straight towards the city line. The overview of house sewer line is a long "L" shape.

Incident #1
Flushed #3 toilet overflowed with backup in bath#3 shower. There were bubbles in bath#2 toilet at same time. Used Draino in shower and Rooter Co. came next day. Video through small internal cleanout behind toilet #2 showed no clog but that could be result of Draino. Rooter plumber recommended bringing up/installing cleanout in front yard for future hydro jetting.

Incident #2
Washing machine draining caused overflow of toilet#1. Heard gurgling sound in kitchen sink at same time. Same rooter co. came and video of toilet#1 showed some tissue blockage which video equipment loosened. Plumber showed me video of what looked like piece of cable caught in pipe 30 ft from entry which may be the culprit. Perhaps cable from previous snaking?

1. Rooter guy can use cutter to grab cable. No guarantee he can pull it out or that it won't break and go downstream.
2. Don't do anything and see how things go now we know what the problem is. Modify habits.
3. Break slab and pull out pipe and cable. (Expensive!!!!)
4. Install 2 cleanouts and hydrojet pipes.

Any advice please? If we install clean out(s), where should it go??? Thank you!