Hola muchacho!

Welcome to FT
I am currently on the Costa del Sol on my current RTW (the joys of retirement)

As Gardyloo pointed out you cannot do all you want to do on a single RTW ticket – because you are allowed to cross the Atlantic (and the Pacific) only once and to achieve what you want would entail crossing the Atlantic three times

Your proposed RTW itinerary is just under 27,000 miles – so you can do it on a LGLOB29, which is less expensive than the LGLOB34 you mentioned
(ex-Eurozone the LGLOB29 base fare is EUR2500 and the LGLOB34 is EUR2900 – source ExpertFlyer)

The LGLOB26 is EUR2110, but I cannot see any way for you to get your mileage down to the maximum 26,000 allowed on that ticket (and also it allows only five stopovers, with a max of two in each region)

The LGLOB29 price ex-Argentina is USD4150, which is ~EUR3720, so significantly more expensive than ex-Europe

So to me it looks like your only option is a Spain-Argentina return ticket followed by an ex-Spain LGOB29

Your itinerary is nearly 27,000 miles and requires 9 segments. So you are ‘leaving on the table’ ~2,000 miles and 7 segments. Depending on your time availability and budget, you could look at adding more flights, for example in

• South America
• The South West Pacific
• Asia
• Africa
• Europe, prior to returning to Spain at the end

Happy planning