The Greek words agree with what you say above:It's too bad some interpreters seem incapable of thinking outside of the box at times. I'm not suggesting they never think outside of the box, I'm only meaning in some cases they apparently don't, otherwise they wouldn't be coming to some of the absurd conclusions they do at times, but would be using Scripture to interpret Scripture instead.
Let's take this thief on the cross, as an example, and let's then pay close attention to what the thief said and what Jesus didn't say.
Luke 23:43 And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise.
Revelation 2:7 He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh will I give to eat of the tree of life, which is in the midst of the paradise of God.
Revelation 22:1 And he shewed me a pure river of water of life, clear as crystal, proceeding out of the throne of God and of the Lamb.
2 In the midst of the street of it, and on either side of the river, was there the tree of life, which bare twelve manner of fruits, and yielded her fruit every month: and the leaves of the tree were for the healing of the nations.
There is obviously a connection here between all of these passages and what the thief said per the following below shows us how they are connected, the fact Christ never corrected him about anything, therefore, there was nothing to be corrected about.
Luke 23:42 And he said unto Jesus, Lord, remember me when thou comest into thy kingdom.
43 And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise.
Obviously, kingdom and paradise are meaning the same thing. Obviously, Christ never came into His kingdom upon death, and that the thief said to remember him when He comes into His kingdom. And that Christ then says---Verily I say unto thee To day, shalt thou be with me in paradise--and not this instead--Verily I say unto thee, To day shalt thou be with me in paradise. Or maybe it even could mean the latter but not the way some typically take it to mean. It could simply mean that that very day, the thief's fate was sealed and assured, that when Christ comes into his kingdom in the future, meaning when the NJ that comes down from God out of heaven, the thief will be in paradise with Him as well.
Otherwise we have to assume utter nonsense, such as Christ coming into His kingdom upon death if we take verse 43 to mean that very same day.
Clearly, both Revelation 2:7 and Revelation 22:1-22 identify the paradise meant in Luke 23:43. Therefore, what Jesus said in verse 43 was prophetic in nature and meaning when He bodily returns in the end of this age, that being when He is coming in His kingdom.
G 3588 O ("The") (Definite article)
G 2250 hemera ("Day")
G4594 semeron ("The day")
-- "And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily I say unto thee, To day (G4594 semeron - "The day") shalt thou be with me in paradise." -- Luke 23:42-43
4594
σήμερον
shvmeron semeron {say'-mer-on}
neuter (as adverb) of a presumed compound of the article 3588 (t changed to s) and 2250; on the (i.e. this) day (or night current or just passed); generally, now (i.e. at present, hitherto):--this (to-)day.
see GREEK for 3588
see GREEK for 2250
-- "And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily I say unto thee, THE DAY shalt thou be with me in paradise." --
So it means what in modern English we would call "on that day".