Why do you think it's beside Hades?
The parable of the Rich man and Lazarus was a parable. The only good theology you can take from it (on this subject) is what is said explicitly.
From it we know that the place of the righteous dead is not the same place that the unrighteous went to before the cross. We would know that intuitively anyway but the parable seems to nail that point down pretty tight and we can also know that there is no way for someone to get from one place to the other because there is a great gulf between them.
To go beyond that and suggest that they are so proximate to each other that one could not be a paradise has no support from any biblical passage whatsoever.
Further, this summary of yours leaves out most of my argument. Jesus not only said He was going to paradise but He also said that He had not ascended to the Father and Paul tells us that He descended to the lower parts of the Earth.
It doesn't sound to me like the Paradise that Jesus Himself said that He went to was in Heaven.
What happens to us happens because Jesus' redemptive work has been completed and because Jesus has both descended and then ascended (Eph. 4, I Cor. 15 & elsewhere), which He had not yet done as of Luke 23.
This the criminal on the cross would have gone to the place of the righteous dead along with the rest of those who were saved throughout the Old Testament.
This ignores Jesus' plain statement...
Luke 23:43 “Assuredly, I say to you, today you will be with Me in Paradise.”
This also ignores the fact that no one could go to the Father prior to Christ's resurrection because the plan of redemption had not yet been accomplished.
To do so would be to take a position beyond what this passage states. Committing something into someone's hands is simply a way of saying that your are turning over that thing to their control. Jesus was telling His Father to do what He will's with His Spirit.
One could choose to take the passage in a woodenly literal way and insist that Jesus went to the Father but that ignores Jesus' own words to the contrary when He told Mary that He hadn't yet done so. He didn't say that He hadn't yet done so "bodily", He just simply said that He hadn't yet done so.
And so, once again, without being overly dogmatic about an issue for which the data is sparse, the position on this that seems to best fit what little data we do have is that Jesus went to Abraham's Bosom, which He called Paradise and which Paul indicates was located in the lower parts of the Earth and which has a great gulf fixed between it and the place of the condemned dead.
I see no good reason to believe otherwise and certainly no reason to insist that anything else is true.
Clete