Sorry for the long reply, I happen to enjoy this subject quite a bit.

The "hierarchy" breaks once you try to analyse it with no regards to governments, focusing solely on linguistic features (phonetic, phonology, syntax, and the expressions). Because of things like this:

• Manezinho (from Florianópolis) and Azorean dialects are clearly a beast apart. They can understand each other, nobody else can understand them. If there's one major division in Portuguese, it got to be Insular with those two and Continental with the others.
• Alentejo usage of -ndo gerunds, a gente, and a partially syllable-timed prosody. Those things are typically associated with BP, not EP.
• Mineiro (BP) often reducing vowels even more aggressively than Estremenho (EP), even if theoretically BP is known for syllable-timed prosody.
• More conservative speakers in Paraná and Santa Catarina not raising the final unstressed vowels (you know, that "dor de dente" [dẽte] meme for Curitiba? That's it), while almost everyone else would raise it to either [ɨ] or [i]. It's a phonemic deal because the raising merges /e o/ and /i u/ in this position. For reference this conservation of the unraised vowels is usually associated with Galician, not even Portuguese. And it's actually a phonemic deal, since the raising triggers a merge for non-conservative speakers in Brazil.
• The dialects in the northern ~half of Brazil (N, NE, chunks of SE) palatalising [s~z] into [ʃ~ʒ], a trait shared with dialects spoken in Portugal, but not with the southern ~half.
• In the same rough area as above you got a coda /ɾ/→/r/ shift. Mattoso Câmara tries to deal with it in a cheesy way, but it's also phonemic in nature, unlike using [ɹ] for /ɾ/.
• Lack of regressive T-palatalisation (/ti/ as [tʃi]) in some chunks of the Brazilian Northeast, in Cuiabá and in some chunks of Santa Catarina. Often with some caveat, like Cuiabano rendering /ʃ/ as [tʃ] instead, some Nordestinos doing progressive palatalisation (e.g. "oito" as [ojtʃu]) and some Catarinas using [ts] instead (e.g. "tia" as [tsiɐ]), that's clearly a parallel development.
• Trasmontano still keeping the old /ʃ/ vs. /tʃ/ distinction; e.g. "xícara" with /ʃ/, but "chiar" with /tʃ/.
• A few heavily conservative expressions used in Caipira Portuguese, such as "inda" and "despois". Caipira also merges the original coda /l/ with /ɾ/ instead of /w/ (e.g. "mal" as homophone of "mar", not of "mau")
• The SOV→SVO shift for clitic pronouns (te falar → falar-te) being likely more recent in Portugal than the colonisation of Brazil; for example, check news for the Lisbon earthquake and you'll see SOV being used all the time.

I'm not informed enough on the dialects spoken in Africa to affirm anything about them, but I wouldn't be surprised if that also applied there - for example, Portuguese as spoken in Luanda being actually closer to the one in Lisbon than the one in the Angolan countryside.

And it actually makes sense, when you think about the initial colonisation of Brazil - you had four initial settlements, most people were likely from southern Portugal, and each settlement would undergo independent dialect levelling.

Any hierarchy that we put here would eventually break, by the way. You get a bunch of wave innovations but their pattern usually ties large centres together, regardless of country, with rural varieties either adopting those features later or developing alternative ones. But if we must see it on a hierarchical way, the split wouldn't follow country borders, it would be more like:

• Galician-Portuguese → Galician + Portuguese
• Portuguese → Coimbra-Lisbon + "a gente" dialects (southern Portugal and Brazil)
• "a gente" dialects → coda-/r/ dialects (northern half of Brazil) vs. coda-/ɾ/ (southern half of Brazil + Alentejo and the Algarve)

Note how the division actually lumps Alentejano and Algarviano alongside what you'd call BP, not EP. And note how it still breaks, for example the /ʃ/ coda in the northern half of Brazil was likely interference from Estremenho, even if both dialects would be relatively far from each other in the hierarchy.

Oh right, I hadn't thought about it!

Funilly enough and if I remember it correctly, a pila is a kind of throwable spear from the Roman times.

You might be into something here. The spear is pilum, and Portuguese reborrowed it as pilo. However Portuguese used to repurpose the gender change for specific types of something, specially for Latin neuter words: see ovo/ova, casco/casca, jarro/jarra, barco/barca. It's possible that the slang appeared this way, with people referring to their dicks as a type of spear. (It's kind of childish but fairly common; c.f. caralho from caraculum "small mast")

There's also another Latin pila meaning mortar, but it got inherited by Portuguese as pia "sink".

(IIRC pila-as-money is from a politician, Raul Pilla.)