As a native speaker I assure you that 請 is pronounced differently in context, and that both readings are perfectly Cantonese.
For a more clear example, see 平: 大平賣 ("vernacular" reading; peng4) (lit. big cheap sale; i.e. sale) vs 平面 ("literary" reading; ping4) (lit. flat surface; i.e. surface). peng4 is the "vernacular" reading but used exclusively for meaning cheap. ping4 is "literary" but used everywhere else. "vernacular" versus "literary" is a linguistic classification, but do not necessarily represent either being more common than the other reading. Both readings exist.
I'm happy to hear that both can be used, normally I always have heard more of the "e" shift in a relatively consistent way. I normally say "大減價" for a big sale, but I understand your point was more about showing a demonstration where the "i" may be used. Although I would say that it really depends on the speaker and how they feel. I would most likely use the "e" shift consistently and be perfectly understood.
The example is meant to demonstrate that whether I say 平 as ping or peng changes the meaning of the sentence. It does not depend on how I feel like it.
Another example: I buy some raisins, and the lady gives me some. I say: 咁多！ If I pronounce "gam3do1", I say "That's so much!". If I pronounce "gam3doe1", I say "That's so little!".
(Yes, contrived. Almost always the former is used. But both can be.)
For a more clear example, see 平: 大平賣 ("vernacular" reading; peng4) (lit. big cheap sale; i.e. sale) vs 平面 ("literary" reading; ping4) (lit. flat surface; i.e. surface). peng4 is the "vernacular" reading but used exclusively for meaning cheap. ping4 is "literary" but used everywhere else. "vernacular" versus "literary" is a linguistic classification, but do not necessarily represent either being more common than the other reading. Both readings exist.