Welcome to Ft ThePeripateticOne

Your itinerary has no flaws, but I'm intrigued by what the brackets mean - for example "SCL-(SYD-BNE)-NOU"

With your BNE and SYD stops, I presume you're located somewhere on the East coast of the lucky country, and further that you want to start in Asia so that you can get two trips out of the one ticket (the first being RTW from SIN to Oz, and the 2nd to HKG and XIY)
BUT, I'll just point out that one of the cheapest places to start a LONEn is from New Zealand - for example ex-SIN LONE4 base fare SGD5419 and ex-AKL NZD3899 (the SGD:NZD exchange rate is 1:1) - so a saving of NZD/SGD1520 by starting in AKL

Your first segment is SIN-LHR, so that must be on either QF or BA - both of which are known for their hefty fuel surcharges. If you started with say SIN-HKG-CDG..., and so CX will be your first carrier, then your surcharges should be greatly reduced - try it using the on-line tool
Same thing if you choose to start from AKL - start with AKL-HKG on CX to reduce the surcharges

People ticket through AA for two basic reasons - historically AA has imposed very few fuel surcharges (though this is no longer as good as it used to be), and AA has a good RTW desk which makes it easy to set up the ticket and to make subsequent changes to it (at no fee)

I'm not sure if open-dated tickets are still possible

Under the ticket rules, date, time and carrier changes are allowed free of charge (a date change is subject to the 1 year time limit between the first and last flights) - but airlines can impose a service fee, which is what QF does

Other:
You're intending to fly LIM-LPB!!??
Fly over the Sacred Valley/Macchu Pichu and Lake Titicaca!
In March this year we bought cheap add-on flights LIM-CUZ (and bus/train return to Macchu Pichu through the valley) and CUZ-JUL (then bus to Puno on the shore of the lake, and then bus on to La Paz)

Booking class L seats are hard to find on the southern trans-pacific flights (QF SCL-SYD and LA SCL-AKL/SYD)

Happy planning