I disagree that your notion more credible and to the is indeed as simple as Kurama undoubtedly having the most chakra of all of the bijuu. Half of Kurama is at least 5x‘s stronger than Gyuki, even KCM Naruto’s power was immaculate compared to Bee’s V1 & 2 transformations. Kurama having the most chakra makes him the most akin to the Juubi, hence his 9 tails. That’s also why Naruto and Minato both took on Juubi jin-esque features when using their BCM cloaks. Additionally that’s why the bijuu had to be gathered and sealed within the Mezo in order because Kurama‘s power dwarfs all of the others.
Another aspect to look at is Kurama’s life force power, which caused Minato’s wood constructs grow leaves. It’s like as the Mezo itself and the Juubi.
I can't really agree that simply having more chakara would yield six paths esque properties, even if the amount of chakara dwarfs that of the other bijuus.
We never see characters gain entire modes or new properties just from the quantity of chakara. It is generally the type of chakara that grants new powers and features (not the quantity).
Examples:
We see several characters gain modes such as sage mode or curse mark modes from the acquisition and utilization of natural energy, which is a different type of energy than normal chakara. We never see someone just suddenly gain sage mode or a curse mark mode from simply having a lot of chakara.
Another example is how we see jinchuuriki gain special cloaks and modes from using bijuu chakara, which is a different type of chakara from normal chakara. Even non-jinchuuriki have manifested bijuu cloaks when given some bijuu chakara (referencing when Naruto gave the alliance cloaks). Of course, no non-jinchuuriki shinobi is going to manifest a bijuu cloak just by simply having a lot of chakara. This is another example of how the type of chakara grants new powers and modes, and not the quantity.
Another example is with six paths chakara. We have seen six paths chakara do things such as turn raiton techniques black (and more powerful), and allow a person to actually attack limbo. Simply having large quantities of regular chakara won't yield these results.
We even see this concept with dojutsu since it takes a special type of chakara released from an Uchiha's brain to awaken the sharingan (an effect that cannot be achieved simply by having large quantities of chakara).
The overarching pattern here seems to be that type of chakara yields new modes and powers rather than quantity.
Having said that, I would see it as more likely that Kurama has those special qualities because of Hagoromo doing something to him rather than simply having more chakara than the other bijuus.
Besides, like I said before, if what you say is true then it would still make more sense for him to say Indra + Asura + juubi.
Edit:
It is also worth noting that Kurama's modes are similar to Asura's mode (who possessed rikudou chakara) and Asura wasn't even a jinchuuriki.