I tend to agree with your three specific objections:
- 5 vowels is actually a very good choice (although the diphthongs in Esperanto are notably odd)
- pronouncing the R differently is unavoidable and probably fine
- the x-method works okay in practice (although I subjectively don’t really like it)
The linked page is “the page” on the problems with Esperanto, and I still think that it has a lot of insight, even if I don’t agree with every point he makes.
For example, I had no idea how much East Slavic grammar influenced Esperanto, or how important word order was in practice for complex sentences.
I think it’s reasonable that a much better IAL than Esperanto could be designed today, given all the knowledge of linguistics that we now have, and all of the experienced conlangers. I don’t think that Esperanto is so good that surpassing it would be “one huge nirvana fallacy”.
But I also don’t expect anyone to ever make an IAL that is more successful than Esperanto, because Esperanto’s success was a product of its time.
Nowadays, with the status of English, and the availability of machine translation, an IAL is just less important than it once was.
On a positive note: I recommend the book “In the Land of Invented Languages” by Arika Okrent for a history of conlangs.
As a shibboleth, here is a sample of my own shitty conlang, whose design I will not attempt to defend:
anu, ʃamuti usli bisini uma kamlusu slapluŋwu ixla dwamuʒu aku pluŋwuslu bisana aku
pwanusu ʒapwunu aku pumuʃwu ixla bluŋusu ʃwutuŋu aku pluŋwuslu aʃa ʒubunlu
dimivi… azi ʃumuti ivwu sunwubi xubuŋu bisini uma ʒamigi ivwu vamidi idu bisini
bunluʒu xudwunu iza. ʒamigi ivwu vamidi idu bisini uma bisini sudumu fupumu fupumu
uta βubunu uta ʃutwumu itu tunuʒu ixla buʒunlu. kiŋliɣi ixla tiniʒi guŋuʒu iba: ʃamiti
kiɣiŋi uma mlupuʃu, iʒi igi vabwiŋli ʃubunu uta afu, iʒi xinlipi baʒinli mlupuʃu, azi
xunlapa usli bisini mlupuʃu. ʒlumlaga bisini ŋlagusu bisana ibi vwadluŋlu itu xunlapa
bisini ŋuguʒu, azi vaŋupa usli, iʒa zwuŋika ivwu suŋibwa bisini ŋladluvwu ixla ŋatuɣwu.
udi ʒiŋiti biʒinli busini paŋuɸu xwaguŋu uŋwa ʒabunlu iʒi ʃumuti ivwu sunwubi xwuguŋu
bisini uma xanlipi bisini ŋuguʒu. dwinixi iba. iʒi xaŋiti bisini. diŋixwi ixla paŋiɸi xwagiŋi
vwiŋigi ivwu sinwibi guŋuʃu bisana, paŋiɸi uŋwa kaŋiɣli pamluzu.