Main (?) Drain Issue

[Chunkah]

So I did a load of laundry yesterday and as the machine drained it overflowed out of the drain and partially soaked the basement floor. This has happened before. Last time it was due to a Lego guy (got 3 kids in the house) and a big hunk of lint stuck in the drain. Once the obstruction was removed all was well....this time no such luck. Now it seems that if we use any water it backs up out of the same washing machine drain location. Run the kitchen sink for 20 seconds it backs up. Flush the toilet, it backs up. SO far things seem to be pretty clean in terms of water backing up, but now since the toilet is involved I'm really not sure how long that's going to be the case. I put a call in to my plumber in the hopes that i can get on the schedule for first thing tomorrow. My first question is this. The kitchen sink and wash machine drain through a 2" copper line. My toilet, tub, and bathroom sink (2nd floor) drain through the main 4" stack. Since both cause a water backup at the lowest open point, that being my basement washing machine drain, is it safe to assume that the clog is beyond where the two drain lines intersect? This is my assumption as of now. There is only maybe 5' of 4" drain after the two intersect before the 4" main exits the building. Within that 5' section there is a cleanout on the top of the pipe. There is also three rubber unions (my terminology is probably off here)...two on the house side of the cleanout, and one on the street side of the cleanout. The problem is that this area is under my existing basement stairs (100+ year old house) and there is almost no way to effectively access that area of piping without either ripping out 1/2 my basement stairs, or being a bit of a contortionist and working on it as it is. Not being a plumber I'm not sure if it's worth trying on my own. In a nearly perfect world I'd act like a contortionist, remove a section of the existing 4" drain, probaly the part that holds the cleanout, use a bladder to try to blow out the street side of the pipe, snake out the house side of the pipe, and then replace the removed section of cast iron with a new section of PVC and two new rubber unions. In a perfect world I would remove the furthestmost union towards the street, remove the connection where the 2" copper drain connects to the main drain, break the existing main (making a clean break concerns me A LOT) at the existing elbow where it turns vertical, blow out the existing street side main with a bladder, then using rubber unions replace the entire run of main drain with PVC being sure to reconnect the 2" copper drain and installing 2 cleanouts....one where the elbow is now, and one just beyond where the 2" drain enters the 4" main.
So I guess the overall question is should I attempt to do this myself, or should I leave it to the plumber? Keep in mind I can solder a joint, trap a sink, install a hot water heater, and am a GC, so I am not a total dummy when it comes to this stuff, but I am not a plumber. It seems pretty straight forward, and I'd love to save myself a considerable amount of $$, but again, I'm not a plumber and breaking the 4" cast iron main cleanly makes me nervous.
So, do you think I should try it on my own? Do you think my assumption of the location of the problem seems correct?
Thanks!