If you don't have GFCI now, I'd say there's no loss in safety and it's all gain.
The real question is whether you want the current situation, where you can plug two fat 1500W loads into the 2 sockets of one receptacle, and not get a breaker trip. That is to say, if you call your 2 circuits A and B, do you want your sockets to have a circuit configuration of
A___________A or would you rather have A____________B
B B A B
If you want the left one, your only option is to leave the sockets wired as they are, and fit a 2-pole GFCI breaker in the service panel. This is guaranteed to protect the whole circuit, unless there's a wiring fault, in which case it will never stop tripping.
If the right one is fine with you, then your choice is GFCI receptacles, and "skip socket" wiring as in the question you linked. However, very important! If the next socket downline is wired with /3 cable (including a red wire), then you cannot use the
LOAD terminals on the GFCI at all: leave the warning tape on them. Regardless, you must always pigtail since you only have 1 screw on the GFCI (neutral should already be pigtailed if the rules were followed).