My experience - make the effort to attempt recovery of the lock ring mechanically with the wellhead hanger running & retrieving tool. Not sure but I my experience I have not heard of ROV's being able to unlock 13.3/8" casing hangers. ?
Multi string cutting like this has it's issues. Namely if the 13.3/8" casing is not cemented that high up then there is a risk (small to medium) of backing off the casing coupling above the cut point as the knives sweep up and out. The cutter turns to the right (as we all know) but if the casing parts in tension when it is just cut - the energy from the tension release induces a blind back off type effect from the coupling above. When this happens the casing is then free to slide down from the backed off coupling above and it will swallow the cutter - then you just sit there spinning free. End of Cut! Mobilise explosives or abrasives or you may end up with serious milling work to do....
Multi string cuts can be done in one run but be prepared to need a 2nd cut to finish the job - allow the BHA to contain a spacer sub that can be removed from the contingency 2nd cut run that allows the cutter to re-enter the original window with longer knives. The 11.5" - 12" OD cutters used for this are at their limitations so knive length is critical to allow the cut out and milling up process inside 12.415" casing ID. If the knives are too long then it is impossible to obtain that 'cut out' with all the pump pressure in the world.
If your multi string cut is successful, I recommend using the 18.3/4" wellhead running & retrieving tool to recover 13.3/8" x 20" x 30" casings. Spears give you the added worry of something cutting loose in the splash zone or cellar deck as you recover.