You only use the original Damage dice

The Chaos Bolt new target determination is only based off of the original 2d8 of the damage - not the additional d8s from the Critical Hit. The critical damage is extra damage and the language of Chaos Bolt is clear in it's line (emphasis mine):

If you roll the same number on both D8s

This is also supported by this tweet from Jeremy Crawford:

The chance for chaos bolt to jump to another target is not lessened by a critical hit. The spell's text says you look at "both d8s"—that's the two dice in the spell itself, not extra dice added from another rule

The idea of Extra Dice is supported by the PHB wording (page 196)

When you score a critical hit, you get to roll extra dice for the attack's damage against the target.

It is the next sentence that delivers the total damage and is clear that it's separate from the prior sentence:

Roll all of the attack's damage dice twice and add them together. Then add any relevant modifiers as normal.

There's no perfect way to assign rarities to all the tables.

I made a spreadsheet counting the percentage of items of each rarity¹ contained in each of tables A through I. These results are as follows.

\$ \begin{array} {c|r|r|r|r|r} \textbf{Table} & \text{Common} & \text{Uncommon} & \text{Rare} & \text{Very Rare} & \text{Legendary} \\ \hline \textbf{A} & 50\% & 50\% & & & \\ \hline \textbf{B} & & 100\% & & & \\ \hline \textbf{C} & & 14.3\% & 85.7\% & & \\ \hline \textbf{D} & & & 6.3\% & 93.8\% & \\ \hline \textbf{E} & & & & 42.9\% & 57.1\% \\ \hline \textbf{F} & & 100\% & & & \\ \hline \textbf{G} & & 2.1\% & 96.8\% & 1.1\% & \\ \hline \textbf{H} & & 2.9\% & 8.7\% & 88.4\% & \\ \hline \textbf{I} & & & 7.8\% & 23.4\% & 68.8\% \\ \end{array} \$

As can be seen, only tables B and F are completely consistent in their rarity, so it's not possible to assign a rarity to every lettered table perfectly.

But there's a better way to solve the problem.

The problem isn't really what rarity to assign each lettered table. It's how to preserve which rarities become available to a character when they reach a specific tier and at a particular point cost (according to the Shared Campaign rules being used). For example, it doesn't matter that table I contains a mix of very rares and legendaries. What matters is that major legendaries only become available at tier 3 for 12 points, and only table I has them, so for all practical purposes when a character becomes eligible for table I then they become eligible for major legendaries.

So, how to solve that version of the problem...

1. Observe when each minor and major rarity becomes available to a character for the first time based on tier requirements, grouping any rarities that share a tier requirement and point cost.

2. Observe which lettered tables cover each minor and major rarity most precisely, grouping any tables that share a tier requirement and point cost.

3. See if we can find an obvious mapping from the table groups in step 2 to the rarity groups in step 1. If so, we can refactor the purchase options.

My observations for the minor items are as follows.

• Commons, uncommons, and rares start at tier 1 for 4 points. Tables A, B, and C (plus the minor commons in Xanathar's) almost perfectly² cover these rarities.
• Very rares start at tier 2 for 8 points. Table D almost perfectly² covers this rarity.
• Legendaries start at tier 3 for 8 points. This rarity is exclusive to table E.

My observations for the major items are as follows.

• There are no commons.
• Uncommons start at tier 1 for 8 points. Table F almost perfectly² covers this rarity.
• Rares start at tier 2 for 10 points. Table G almost perfectly² covers this rarity.
• Very rares start at 3 for 10 points. Table H almost perfectly² covers this rarity.
• Legendaries start at tier 3 for 12 points. This rarity is exclusive to table I.

I think an obvious mapping has emerged: in the table of magic item purchase options in Xanathar's (p. 174), replace each of the lettered tables with the following minor/major rarities and then ignore tables A to I in favor of the minor/major rarity tables in Xanathar's.

• A, B, and C (as a group): minor common, minor uncommon, and minor rare.
• D: minor very rare.
• E: minor legendary.
• F: major uncommon.
• G: major rare.
• H: major very rare.
• I: major legendary.

Although this mapping is not exactly equivalent to the way the purchase options were originally presented, the scenarios where a player could buy an item earlier or later than the original options allowed are essentially edge cases that balance each other out.

This mapping ought to allow the players to use the tables in Xanathar's instead of the DMG's tables A through I easily without deviating greatly from the balance apparently intended in the original options, which was the real problem to begin with.

Footnotes on My Methods

1. These percentages are according to the rarity of the item names listed in the table, not the probability of randomly generating an item of each rarity using the table's d100 column, since we're not trying to generate random treasure. Data entry errors should be insignificant.

2. When I say "almost perfectly" I mean there are on the order of 5 outliers out of just under 400 entries, which is insignificant. Note that by "entries" I mean the number of item names listed in the tables preserving duplicates across tables, not the number of unique items described in the book, which is far fewer.