No, there is no chart you are not finding!
When we are naming a chord we stick to, for ease, naming in relation to the major scale. In this way we can communicate a chord 'spelling' to one another in a way that is separate to any key the chord may be used in. We can also just describe a chord, free from it's association to a given key, and use it in any other key of the students desire. In that way we can also be sure that when I say 'a third' or 'a flat seventh' we both know exactly what that interval is, how many 'notes up' it is and how to play it on guitar/piano etc.
If there was a second convention of naming against the natural minor scale as well we would have to remember two sets of interval, two types of 3rd for example, and when communicating a chord spelling we would have to be sure to say wether it was major or it's minor counterpart.
Historically, I have read publications from 300 years or so ago where they don't specify 3rd or b3rd, they just say 3rd, and it's up to the learner to remember that we are in a minor tonality, or indeed we are playing one of the minor chords in a major tonality (Emin in the key of Cmaj for example). Over time however, it's become convention just to always stick to the same interval names (there are exceptions, #5 / b13 for example but thats a very different case).
As such when we are in a minor key we don't rename the intervals in respect to that new minor scale. The 3rd note up from the tonic in a minor key is a b3rd, even though it's the third note of and natural to that particular key.
When naming the intervals we are using the major scale as a kind of yardstick to be able to describe where they are in relation to a given root point. You always use the major scale to name the intervals even if you are in a minor key, or in some other deeply exotic key or indeed you are playing completely a-tonally.
(think of what b3rd means, it's saying 'find the 3rd you get in a major scale, then flatten it'. Similarly, 'my melody is 1 b5 b6 7 7 b2 5 b7 ... ' etc. I'm just describing where those notes lay in relation to a major scale, despite it not being in a major key at all, note the scale / key terminology distinction there)
Chord naming uses major scale to describe, intervallic-ally, whats going on in that very moment, in the next bar and the next chord there's a new root note and if we wanted to name THAT chord we start again, laying a major scale over the top of this new chord to work out the intervals.
Similarly, if we look at the triads constructed in a given major key the first chord is of course '1 3 5', the second chord is NOT '2 4 6', that would be hideously complicated and un-useful! We know it's the 2 chord, or II, but we still name it's root note as '1st' and then work out the intervals of a b3rd and 5th to complete the II chord. So you can see again we are just using the major scale as our 'interval ruler' regardless of what tonality a piece is in and regardless of what chord from what key we are currently playing.
In short, this is for simplicity of learning, and simplicity of communication. Music theory is convoluted, but ultimately about getting across the information as clearly as possible, if we needed to remember a different way of naming chords for major and minor tonalities that would just add potential for confusion.
I'm not going to go any further working out the chords in the way you mention because of the reasons above, it's not the way musicians communicate and would be confusing if so, however by all means have a go for the thought exercise, but if you are fairly new to theory don't get too bogged down in it as it's a road that may confuse and certainly won't help that much with learning the 'mainstream' system. Also Aaron it seems has already done a good job of working out the chords in the proposed system!